references.bib

% ********************************************************************
%                             IGA 
% ********************************************************************
@Article{Garoni2014,
author="Garoni, Carlo
and Manni, Carla
and Pelosi, Francesca
and Serra-Capizzano, Stefano
and Speleers, Hendrik",
title="On the spectrum of stiffness matrices arising from isogeometric analysis",
journal="Numerische Mathematik",
year="2014",
volume="127",
number="4",
pages="751--799",
issn="0945-3245",
doi="10.1007/s00211-013-0600-2",
url="http://dx.doi.org/10.1007/s00211-013-0600-2"
}


@book{DeBoor_Book2001,
  title={A Practical Guide to Splines},
  author={de Boor, C.},
  isbn={9780387953663},
  lccn={20049644},
  series={Applied Mathematical Sciences},
  url={https://books.google.de/books?id=m0QDJvBI\_ecC},
  year={2001},
  publisher={Springer New York}
}


@article{Ratnani2012,
title = "An Isogeometric Analysis Approach for the study of the gyrokinetic quasi-neutrality equation",
author = "Crouseilles, N. and Ratnani, A. and Sonnendr{\"u}cker, E. ",
journal = "Journal of Computational Physics",
volume = "231",
year = "2012",
pages = "373-393"
}

@article{Hughes_CMAME2005,
  title={{Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement}},
  author={Hughes, TJR and Cottrell, JA and Bazilevs, Y.},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={194},
  number={39-41},
  pages={4135--4195},
  year={2005},
  publisher={Elsevier}
}

@article{vanderZee:2011,
 author = {van der Zee, K. G. and Verhoosel, C. V.},
 title = {Isogeometric analysis-based goal-oriented error estimation for free-boundary problems},
 journal = {Finite Elem. Anal. Des.},
 issue_date = {June, 2011},
 volume = {47},
 issue = {6},
 month = {June},
 year = {2011},
 issn = {0168-874X},
 pages = {600--609},
 numpages = {10},
 url = {http://dx.doi.org/10.1016/j.finel.2010.12.013},
 doi = {http://dx.doi.org/10.1016/j.finel.2010.12.013},
 acmid = {1968380},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 keywords = {A posteriori error estimation, B\'{e}zier extraction, B-splines, Bernoulli free boundary problem, Duality, Goal-oriented analysis, Isogeometric analysis, Non-uniform rational B-splines (NURBS), Shape-linearized adjoint, T-splines},
}

@article{isopic,
     author = {{Back, A.} and {Crestetto, A.} and {Ratnani, A.} and 
{Sonnendr\"ucker, E.}},
     encoding = {tex},
     title = {An axisymmetric PIC code based on isogeometric analysis},
     DOI= "10.1051/proc/2011016",
     url= "http://dx.doi.org/10.1051/proc/2011016",
     journal = {ESAIM: Proc.},
     year = 2011,
     volume = 32,
     pages = "118-133",
     month = "",
}
@inproceedings{aigner2009,
 author = {Aigner, M. and Heinrich, C. and J\"{u}ttler, B. and Pilgerstorfer, E. and Simeon, B. and Vuong, A. -V.},
 title = {Swept Volume Parameterization for Isogeometric Analysis},
 booktitle = {Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII},
 year = {2009},
 isbn = {978-3-642-03595-1},
 location = {York, UK},
 pages = {19--44},
 numpages = {26},
 url = {http://dx.doi.org/10.1007/978-3-642-03596-8_2},
 doi = {http://dx.doi.org/10.1007/978-3-642-03596-8_2},
 acmid = {1617226},
 publisher = {Springer-Verlag},
 address = {Berlin, Heidelberg},
}

@article{Cohen2010,
title = "Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "5-8",
pages = "334 - 356",
year = "2010",
note = "Computational Geometry and Analysis",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2009.09.010",
url = "http://www.sciencedirect.com/science/article/B6V29-4X723W2-1/2/642667ab58e119a1fcb6bbdff69ec9d4",
author = "E. Cohen and T. Martin and R.M. Kirby and T. Lyche and R.F. Riesenfeld",
}

@article{Martin2009,
title = "Volumetric parameterization and trivariate B-spline fitting using harmonic functions",
journal = "Computer Aided Geometric Design",
volume = "26",
number = "6",
pages = "648 - 664",
year = "2009",
note = "Solid and Physical Modeling 2008, ACM Symposium on Solid and Physical Modeling and Applications",
issn = "0167-8396",
doi = "DOI: 10.1016/j.cagd.2008.09.008",
url = "http://www.sciencedirect.com/science/article/B6TYN-4TMSNPM-1/2/45c66454560d9be97f96861234bccd38",
author = "T. Martin and E. Cohen and R.M. Kirby",
}

@article{Buffa2011a,
  author    = {A. Buffa and
               J. Rivas and
               G. Sangalli and
               R. V{\'a}zquez},
  title     = {Isogeometric Discrete Differential Forms in Three Dimensions},
  journal   = {SIAM J. Numerical Analysis},
  volume    = {49},
  number    = {2},
  year      = {2011},
  pages     = {818-844},
  ee        = {http://dx.doi.org/10.1137/100786708},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

@article{prautzsch,
 author = {Prautzsch, Hartmut and Piper, Bruce},
 title = {A fast algorithm to raise the degree of spline curves},
 journal = {Comput. Aided Geom. Des.},
 volume = {8},
 issue = {4},
 month = {October},
 year = {1991},
 issn = {0167-8396},
 pages = {253--265},
 numpages = {13},
 url = {http://portal.acm.org/citation.cfm?id=124930.124932},
 doi = {10.1016/0167-8396(91)90015-4},
 acmid = {124932},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
}



@article{Ratnani2011,
   author = {A. Ratnani and E. Sonnendr\"ucker},
   affiliation = {Project-team CALVI, INRIA Nancy Grand Est, 7 rue René Descartes, 67084 Strasbourg Cedex, France},
   title = {An Arbitrary High-Order Spline Finite Element Solver for the Time Domain Maxwell Equations},
   journal = {Journal of Scientific Computing},
   publisher = {Springer Netherlands},
   issn = {0885-7474},
   keyword = {Mathematics and Statistics},
   pages = {1-20},
   url = {http://dx.doi.org/10.1007/s10915-011-9500-8},
   note = {10.1007/s10915-011-9500-8},
   year = {2011}
}

@article{hughes,
title = "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "194",
number = "39-41",
pages = "4135 - 4195",
year = "2005",
note = "",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2004.10.008",
url = "http://www.sciencedirect.com/science/article/B6V29-4FC3S28-1/2/b41b2f3cb1f4023f71e63973d6f2f363",
author = "T.J.R. Hughes and J.A. Cottrell and Y. Bazilevs",
}



@article{hughes3,
title = "Efficient quadrature for NURBS-based isogeometric analysis",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "5-8",
pages = "301 - 313",
year = "2010",
note = "Computational Geometry and Analysis",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2008.12.004",
url = "http://www.sciencedirect.com/science/article/B6V29-4V75YNJ-1/2/a88a102a5291e66436f127c234077e1e",
author = "T.J.R. Hughes and A. Reali and G. Sangalli",
}


@article{ma,
   author = {Ma, W. and Kruth, J. -P.},
   affiliation = {Department of Manufacturing Engineering and Engineering Management City University of Hong Kong 83 Tat Chee Avenue Kowloon, Hong Kong},
   title = {NURBS curve and surface fitting for reverse engineering},
   journal = {The International Journal of Advanced Manufacturing Technology},
   publisher = {Springer London},
   issn = {0268-3768},
   keyword = {Computer Science},
   pages = {918-927},
   volume = {14},
   issue = {12},
   url = {http://dx.doi.org/10.1007/BF01179082},
   note = {10.1007/BF01179082},
   year = {1998}
}

@article{dorfel,
title = "Adaptive isogeometric analysis by local h-refinement with T-splines",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "5-8",
pages = "264 - 275",
year = "2010",
note = "Computational Geometry and Analysis",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2008.07.012",
url = "http://www.sciencedirect.com/science/article/B6V29-4T4XR74-1/2/f53ba4dc17c55b8c46063209cdd55d63",
author = "Michael R. Dšrfel and Bert JŸttler and Bernd Simeon",
}

@article{evans,
title = "n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "198",
number = "21-26",
pages = "1726 - 1741",
year = "2009",
note = "Advances in Simulation-Based Engineering Sciences - Honoring J. Tinsley Oden",
issn = "0045-7825",
doi = "DOI: 10.1016/j.cma.2009.01.021",
url = "http://www.sciencedirect.com/science/article/B6V29-4VJ4WKD-1/2/4615fdbd23872b679a539bd1e9487b14",
author = "John A. Evans and Yuri Bazilevs and Ivo Babuska and Thomas J.R. Hughes",
}

@book{hughes2_book,
  title={Isogeometric Analysis, toward Integration of CAD and FEA},
  author={J.A Cottrell and T. Hughes and Y. Bazilevs},
  publisher={John Wiley \& Sons, Ltd },
  edition = {first},
  year={2009}
}

@article{simeon_2011,
title = "A hierarchical approach to adaptive local refinement in isogeometric analysis",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "49-52",
pages = "3554 - 3567",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.09.004",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511002933",
author = "A.-V. Vuong and C. Giannelli and B. Juttler and B. Simeon",
}

@article{Costantini_Manni_Pelosi_Sampoli_2010,
 author = {Costantini, Paolo and Manni, Carla and Pelosi, Francesca and Sampoli, M. Lucia},
 title = {Quasi-interpolation in isogeometric analysis based on generalized B-splines},
 journal = {Comput. Aided Geom. Des.},
 volume = {27},
 issue = {8},
 month = {November},
 year = {2010},
 issn = {0167-8396},
 pages = {656--668},
 numpages = {13},
 url = {http://dx.doi.org/10.1016/j.cagd.2010.07.004},
 doi = {http://dx.doi.org/10.1016/j.cagd.2010.07.004},
 acmid = {1866637},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
 keywords = {Generalized B-splines, Isogeometric analysis, Quasi-interpolation},
}

@article{Buffa2009a, 
Author = {A. Buffa and G. Sangalli and R. Vazquez}, 
Journal = {Comput. Methods Appl. Mech. Engrg}, 
Pages = {1143--1152}, 
Title = {Isogeometric analysis in electromagnetics: B-splines approximation}, 
Volume = {199}, 
Year = {2009}
}


@article{Buffa2, 
Author = {A. Buffa and J. Rivas and G. Sangalli and R. Vazquez}, 
Note = {Technical report, IMATI-CNR}, 
Title = {Isogeometric Analysis in Electromagnetics: theory and testing}
}

@article{Buffa2011b,
author = {Buffa, A. and de Falco, C. and Sangalli, G.},
title = {IsoGeometric Analysis: Stable elements for the 2D Stokes equation},
journal = {International Journal for Numerical Methods in Fluids},
volume = {65},
number = {11-12},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0363},
url = {http://dx.doi.org/10.1002/fld.2337},
doi = {10.1002/fld.2337},
pages = {1407--1422},
keywords = {IsoGeometric Analysis, NURBS, stability, incompressibility, Stokes flow},
year = {2011},
}

@article{Hughes2006a, 
Author = {T.J.R. Hughes and Y. Bazilevs and L. Beir\`ao de Veiga and J.A. Cottrell and G. Sangalli}, 
Journal = {Mathematical Models and Methods in Applied Sciences (M3AS)}, 
Pages = {1031--1090}, 
Title = {Isogeometic analysis: approximation, stability and error estimates for h-refined meshes}, 
Volume = {16},
issue={7}, 
Year = {2006}
}

@article{Ratnani_thesis,
 author = {A. Ratnani},
 title = {Isogeometric Analysis in Plasma Physics and Electromagnetism},
 year = {2011},
 url = {http://tel.archives-ouvertes.fr/tel-00628060/en/},
 note = "Phd thesis, INRIA, Universit\'e de Strasbourg. URL : http://tel.archives-ouvertes.fr/tel-00628060/en/"
}

@article{pigasus,
author = "A. Ratnani",
title = "Pigasus : Python for IsoGeometric AnalysiS and Unified Simulations",
note = "INRIA report: http://hal.inria.fr/hal-00769225/"
}


@article{pigasus_github,
author = "A. Ratnani",
title = "Python for IsoGeometric Analysis",
note = "https://github.com/ratnania/pigasus/tree/devel"
}

@article{caid,
author = "A. Ratnani",
title = "CAID : A CAD tool for IsoGeometric Computational domains",
note = "INRIA report: In preparation"
}

@article{caid_github,
author = "A. Ratnani",
title = "CAID : Computer Aided Isogeometric Design tool using Python",
note = "https://github.com/ratnania/caid/tree/devel"
}


@article{ratnani_mesh_plasma,
author = "A. Ratnani",
title = "Mesh Generator for 2D Plasma Modeling",
note = "In preparation"
}

@article{Vuong2010,
title = "ISOGAT: A 2D tutorial MATLAB code for Isogeometric Analysis",
journal = "Computer Aided Geometric Design",
volume = "27",
number = "8",
pages = "644 - 655",
year = "2010",
note = "Advances in Applied Geometry",
issn = "0167-8396",
doi = "10.1016/j.cagd.2010.06.006",
url = "http://www.sciencedirect.com/science/article/pii/S0167839610000713",
author = "A.-V. Vuong and Ch. Heinrich and B. Simeon",
keywords = "Isogeometric Analysis",
keywords = "MATLAB",
keywords = "NURBS",
keywords = "Exact geometry",
keywords = "Tutorial code"
}

@article{Gomez2010,
title = "Isogeometric analysis of the isothermal Navier¿Stokes¿Korteweg equations",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "25¿28",
pages = "1828 - 1840",
year = "2010",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2010.02.010",
url = "http://www.sciencedirect.com/science/article/pii/S004578251000068X",
author = "Hector Gomez and Thomas J.R. Hughes and Xesús Nogueira and Victor M. Calo",
}

@article{daVeiga2011b,
title = "Some estimates for h-p-k refinement in Isogeometric Analysis",
journal = "Numerische Matematik",
volume = "118",
pages = "271 - 305",
year = "2011",
note = "",
author = "L. Beirao daVeiga and A. Buffa and J. Rivas and G. Sangalli",
}

@article{deFalco2011,
title = "GeoPDEs: A research tool for Isogeometric Analysis of PDEs",
journal = "Advances in Engineering Software",
volume = "42",
number = "12",
pages = "1020 - 1034",
year = "2011",
note = "",
issn = "0965-9978",
doi = "10.1016/j.advengsoft.2011.06.010",
url = "http://www.sciencedirect.com/science/article/pii/S0965997811001839",
author = "C. de Falco and A. Reali and R. Vázquez",
keywords = "Isogeometric Analysis",
keywords = "Finite element method",
keywords = "NURBS",
keywords = "B-Splines",
keywords = "Matlab",
keywords = "Octave"
}

@article{Manni2011,
title = "Isogeometric analysis in advection¿diffusion problems: Tension splines approximation",
journal = "Journal of Computational and Applied Mathematics",
volume = "236",
number = "4",
pages = "511 - 528",
year = "2011",
note = "International Workshop on Multivariate Approximation and Interpolation with Applications (MAIA 2010)",
issn = "0377-0427",
doi = "10.1016/j.cam.2011.05.029",
url = "http://www.sciencedirect.com/science/article/pii/S037704271100286X",
author = "Carla Manni and Francesca Pelosi and M. Lucia Sampoli",
keywords = "Advection¿diffusion problems",
keywords = "Isogeometric Analysis",
keywords = "Variable degree splines",
keywords = "Exponential splines",
keywords = "Splines in tension"
}

@article{Costantini2010,
title = "Quasi-interpolation in isogeometric analysis based on generalized B-splines",
journal = "Computer Aided Geometric Design",
volume = "27",
number = "8",
pages = "656 - 668",
year = "2010",
note = "Advances in Applied Geometry",
issn = "0167-8396",
doi = "10.1016/j.cagd.2010.07.004",
url = "http://www.sciencedirect.com/science/article/pii/S0167839610000762",
author = "Paolo Costantini and Carla Manni and Francesca Pelosi and M. Lucia Sampoli",
keywords = "Quasi-interpolation",
keywords = "Isogeometric analysis",
keywords = "Generalized B-splines"
}

@article{Manni2011,
title = "Generalized B-splines as a tool in isogeometric analysis",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "5-8",
pages = "867 - 881",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2010.10.010",
url = "http://www.sciencedirect.com/science/article/pii/S0045782510002884",
author = "Carla Manni and Francesca Pelosi and M. Lucia Sampoli",
keywords = "Isogeometric analysis",
keywords = "Generalized B-splines",
keywords = "NURBS",
keywords = "CAD"
}

@article{Farouki2012,
title = "The Bernstein polynomial basis: A centennial retrospective",
journal = "Computer Aided Geometric Design",
volume = "29",
number = "6",
pages = "379 - 419",
year = "2012",
note = "",
issn = "0167-8396",
doi = "10.1016/j.cagd.2012.03.001",
url = "http://www.sciencedirect.com/science/article/pii/S0167839612000192",
author = "Rida T. Farouki",
keywords = "Bernstein basis",
keywords = "Weierstrass theorem",
keywords = "Polynomial approximation",
keywords = "Bézier curves and surfaces",
keywords = "Numerical stability",
keywords = "Polynomial algorithms"
}

@article{Schillinger2012,
title = "An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "",
number = "",
pages = "",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2012.03.017",
url = "http://www.sciencedirect.com/science/article/pii/S004578251200093X",
author = "Dominik Schillinger and Luca Ded\`e and Michael A. Scott and John A. Evans and Michael J. Borden and Ernst Rank and Thomas J.R. Hughes",
keywords = "Isogeometric analysis",
keywords = "Hierarchical refinement",
keywords = "Adaptivity with NURBS",
keywords = "Immersed boundary analysis",
keywords = "Finite cell method",
keywords = "T-spline CAD surfaces"
}

@article{Schillinger2011,
title = "An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "47-48",
pages = "3358 - 3380",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.08.002",
url = "http://www.sciencedirect.com/science/article/pii/S004578251100257X",
author = "Dominik Schillinger and Ernst Rank",
keywords = "High-order B-spline finite elements",
keywords = "Regular grid",
keywords = "Hierarchical refinement",
keywords = "Interface problems",
keywords = "Complex geometries",
keywords = "Finite Cell Method"
}

@article{Collier2012,
title = "The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "213-216",
number = "0",
pages = "353 - 361",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.11.002",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511003392",
author = "Nathan Collier and David Pardo and Lisandro Dalcin and Maciej Paszynski and V.M. Calo",
keywords = "Isogeometric analysis",
keywords = "Direct solvers",
keywords = "Multi-frontal solvers",
keywords = "<span style='font-style: italic'>k</span>-Refinement",
keywords = "Performance"
}

@article{Martin2010,
title = "Volumetric parameterization of complex objects by respecting multiple materials",
journal = "Computers Graphics",
volume = "34",
number = "3",
pages = "187 - 197",
year = "2010",
note = "Shape Modelling International (SMI) Conference 2010",
issn = "0097-8493",
doi = "10.1016/j.cag.2010.03.011",
url = "http://www.sciencedirect.com/science/article/pii/S0097849310000506",
author = "Tobias Martin and Elaine Cohen",
keywords = "Trivariate b-spline modeling and generation",
keywords = "Volumetric parameterization",
keywords = "Model acquisition for simulation"
}

@article{Martin2012,
title = "Mixed-element volume completion from NURBS surfaces",
journal = "Computers Graphics",
volume = "36",
number = "5",
pages = "548 - 554",
year = "2012",
note = "Shape Modeling International (SMI) Conference 2012",
issn = "0097-8493",
doi = "10.1016/j.cag.2012.03.008",
url = "http://www.sciencedirect.com/science/article/pii/S0097849312000477",
author = "Tobias Martin and Elaine Cohen and Robert M. Kirby",
keywords = "Model completion",
keywords = "Volumetric parameterization",
keywords = "Meshing",
keywords = "Physically-based animation and simulation"
}

@article{Wang2011,
title = "Adaptive isogeometric analysis using rational PHT-splines",
journal = "Computer-Aided Design",
volume = "43",
number = "11",
pages = "1438 - 1448",
year = "2011",
note = "Solid and Physical Modeling 2011",
issn = "0010-4485",
doi = "10.1016/j.cad.2011.08.026",
url = "http://www.sciencedirect.com/science/article/pii/S0010448511002259",
author = "Ping Wang and Jinlan Xu and Jiansong Deng and Falai Chen",
keywords = "Isogeometric analysis (IGA)",
keywords = "FEA",
keywords = "PHT-splines",
keywords = "RPHT-splines",
keywords = "Residual-based a posteriori error estimator"
}

@article{NguyenThanh2011,
title = "Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "21-22",
pages = "1892 - 1908",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.01.018",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511000338",
author = "N. Nguyen-Thanh and H. Nguyen-Xuan and S.P.A. Bordas and T. Rabczuk",
keywords = "Isogeometric analysis",
keywords = "T-spline",
keywords = "T-meshes",
keywords = "PHT-spline"
}

@article{Giannelli2012,
title = "THB-splines: The truncated basis for hierarchical splines",
journal = "Computer Aided Geometric Design",
volume = "29",
number = "7",
pages = "485 - 498",
year = "2012",
note = "Geometric Modeling and Processing 2012",
issn = "0167-8396",
doi = "10.1016/j.cagd.2012.03.025",
url = "http://www.sciencedirect.com/science/article/pii/S0167839612000519",
author = "Carlotta Giannelli and Bert Juttler and Hendrik Speleers",
keywords = "Hierarchical tensor¿product B-splines",
keywords = "Truncated basis",
keywords = "Local refinement",
keywords = "Partition of unity"
}

@article{Tian2011,
title = "Adaptive finite element methods for elliptic equations over hierarchical T-meshes",
journal = "Journal of Computational and Applied Mathematics",
volume = "236",
number = "5",
pages = "878 - 891",
year = "2011",
note = "The 7th International Conference on Scientific Computing and Applications, June 13-16, 2010, Dalian, China",
issn = "0377-0427",
doi = "10.1016/j.cam.2011.05.016",
url = "http://www.sciencedirect.com/science/article/pii/S0377042711002639",
author = "Li Tian and Falai Chen and Qiang Du",
keywords = "Numerical PDEs",
keywords = "Adaptive finite element",
keywords = "Adaptive PHT-splines",
keywords = "A posteriori error estimations",
keywords = "Hierarchical T-meshes"
}

@article{Scott2012,
title = "Local refinement of analysis-suitable T-splines",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "213-216",
number = "0",
pages = "206 - 222",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.11.022",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511003689",
author = "M.A. Scott and X. Li and T.W. Sederberg and T.J.R. Hughes",
keywords = "Isogeometric analysis",
keywords = "T-splines",
keywords = "Local refinement",
keywords = "Bézier extraction"
}

@article{Rypl2012,
title = "Object oriented implementation of the T-spline based isogeometric analysis",
journal = "Advances in Engineering Software",
volume = "50",
number = "0",
pages = "137 - 149",
year = "2012",
note = "CIVIL-COMP",
issn = "0965-9978",
doi = "10.1016/j.advengsoft.2012.02.004",
url = "http://www.sciencedirect.com/science/article/pii/S096599781200035X",
author = "Daniel Rypl and Boek Patzák",
keywords = "Isogeometric analysis",
keywords = "B-splines",
keywords = "NURBS",
keywords = "T-splines",
keywords = "Structural analysis",
keywords = "Object oriented environment"
}

@article{XinLi2012,
title = "On linear independence of T-spline blending functions",
journal = "Computer Aided Geometric Design",
volume = "29",
number = "1",
pages = "63 - 76",
year = "2012",
note = "Geometric Constraints and Reasoning",
issn = "0167-8396",
doi = "10.1016/j.cagd.2011.08.005",
url = "http://www.sciencedirect.com/science/article/pii/S0167839611000938",
author = "Xin Li and Jianmin Zheng and Thomas W. Sederberg and Thomas J.R. Hughes and Michael A. Scott",
keywords = "T-splines",
keywords = "Blending functions",
keywords = "Linear independence",
keywords = "NURBS",
keywords = "Isogeometric analysis"
}

@article{daVeiga2011,
title = "IsoGeometric analysis using T-splines on two-patch geometries",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "21-22",
pages = "1787 - 1803",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.02.005",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511000405",
author = "L. Beir\`ao da Veiga and A. Buffa and D. Cho and G. Sangalli",
keywords = "IsoGeometric analysis",
keywords = "T-splines",
keywords = "Approximation",
keywords = "Error estimates"
}

@article{Buffa2012,
title = "Characterization of T-splines with reduced continuity order on T-meshes",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "201-204",
number = "0",
pages = "112 - 126",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.09.005",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511002945",
author = "A. Buffa and D. Cho and M. Kumar",
keywords = "Isogeometric analysis",
keywords = "T-splines",
keywords = "Characterization",
keywords = "Local refinement"
}

@article{daVeiga2012,
title = "Analysis-Suitable T-splines are Dual-Compatible",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "",
number = "0",
pages = " - ",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2012.02.025",
url = "http://www.sciencedirect.com/science/article/pii/S0045782512000679",
author = "L. Beir\`ao da Veiga and A. Buffa and D. Cho and G. Sangalli",
keywords = "Isogeometric analysis",
keywords = "Analysis-Suitable T-splines",
keywords = "Dual-Compatible T-splines",
keywords = "Dual basis"
}

@article{Berdinsky2012,
title = "On the problem of instability in the dimension of a spline space over a T-mesh",
journal = "Computers Graphics",
volume = "36",
number = "5",
pages = "507 - 513",
year = "2012",
note = "Shape Modeling International (SMI) Conference 2012",
issn = "0097-8493",
doi = "10.1016/j.cag.2012.03.005",
url = "http://www.sciencedirect.com/science/article/pii/S0097849312000441",
author = "Dmitry Berdinsky and Min-jae Oh and Tae-wan Kim and Bernard Mourrain",
keywords = "Spline space",
keywords = "T-mesh",
keywords = "Dimension"
}

@article{Xu2011b,
title = "Parameterization of computational domain in isogeometric analysis: Methods and comparison",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "200",
number = "23-24",
pages = "2021 - 2031",
year = "2011",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.03.005",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511001101",
author = "Gang Xu and Bernard Mourrain and R\'egis Duvigneau and Andr\'e Galligo",
keywords = "Isogeometric analysis",
keywords = "Injectivity of B-spline parameterization",
keywords = "Constraint optimization method",
keywords = "A posteriori error estimation",
keywords = "<span style='font-style: italic'>r</span>-Refinement"
}

@article{Ratnani2012b,
  author={A. Ratnani and E. Sonnendr\"ucker},
  title={Isogeometric analysis in reduced magnetohydrodynamics},
  journal={Computational Science \& Discovery},
  volume={5},
  number={1},
  pages={014007},
  url={http://stacks.iop.org/1749-4699/5/i=1/a=014007},
  year={2012},
}

@article{Bazilevs2012,
title = "Isogeometric fluid¿structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "",
number = "0",
pages = " - ",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2012.03.028",
url = "http://www.sciencedirect.com/science/article/pii/S0045782512001041",
author = "Y. Bazilevs and M.-C. Hsu and M.A. Scott",
keywords = "Isogeometric analysis",
keywords = "NURBS",
keywords = "T-splines",
keywords = "Fluid-structure interaction",
keywords = "Non-matching interface discretizations",
keywords = "NREL 5 MW offshore wind turbine rotor"
}

@article{Buffa2010,
title = "Isogeometric analysis in electromagnetics: B-splines approximation",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "17-20",
pages = "1143 - 1152",
year = "2010",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2009.12.002",
url = "http://www.sciencedirect.com/science/article/pii/S0045782509004010",
author = "A. Buffa and G. Sangalli and R. Vázquez",
keywords = "Isogeometric analysis",
keywords = "Compatible schemes",
keywords = "Maxwell equations",
keywords = "Eigenvalue problem"
}

@article{Xu2011a,
title = "Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis",
journal = "Computer-Aided Design",
volume = "",
number = "",
pages = "",
year = "2011",
note = "",
issn = "0010-4485",
doi = "10.1016/j.cad.2011.05.007",
url = "http://www.sciencedirect.com/science/article/pii/S0010448511001175",
author = "Gang Xu and Bernard Mourrain and R\'egis Duvigneau and Andr\'e Galligo",
keywords = "Isogeometric analysis",
keywords = "Analysis-aware parameterization of computational domain",
keywords = "Injectivity",
keywords = "Shape optimization",
keywords = "Steepest descent method"
}
@article{Heinrich2012,
title = "A finite volume method on NURBS geometries and its application in isogeometric fluid¿structure interaction",
journal = "Mathematics and Computers in Simulation",
volume = "82",
number = "9",
pages = "1645 - 1666",
year = "2012",
note = "",
issn = "0378-4754",
doi = "10.1016/j.matcom.2012.03.008",
url = "http://www.sciencedirect.com/science/article/pii/S0378475412000730",
author = "Ch. Heinrich and B. Simeon and St. Boschert",
keywords = "Finite volume method",
keywords = "NURBS",
keywords = "Exact geometry",
keywords = "Navier¿Stokes equations",
keywords = "Fluid¿structure interaction",
keywords = "Matching interface"
}

@article{Shojaee2012,
title = "Free vibration analysis of thin plates by using a NURBS-based isogeometric approach",
journal = "Finite Elements in Analysis and Design",
volume = "61",
number = "0",
pages = "23 - 34",
year = "2012",
note = "",
issn = "0168-874X",
doi = "10.1016/j.finel.2012.06.005",
url = "http://www.sciencedirect.com/science/article/pii/S0168874X12001199",
author = "S. Shojaee and E. Izadpanah and N. Valizadeh and J. Kiendl",
keywords = "Free vibration",
keywords = "Plate",
keywords = "Isogeometric analysis",
keywords = "NURBS",
keywords = "Kirchhoff plate"
}

@article{Bazilevs2010,
title = "Isogeometric analysis using T-splines",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "199",
number = "5-8",
pages = "229 - 263",
year = "2010",
note = "Computational Geometry and Analysis",
issn = "0045-7825",
doi = "10.1016/j.cma.2009.02.036",
url = "http://www.sciencedirect.com/science/article/pii/S0045782509000875",
author = "Y. Bazilevs and V.M. Calo and J.A. Cottrell and J.A. Evans and T.J.R. Hughes and S. Lipton and M.A. Scott and T.W. Sederberg",
keywords = "T-splines",
keywords = "NURBS",
keywords = "Isogeometric analysis",
keywords = "CAD",
keywords = "FEA",
keywords = "Fluid dynamics",
keywords = "Structural analysis",
keywords = "PB-splines"
}

@article{Bornemann2013,
title = "A subdivision-based implementation of the hierarchical b-spline finite element method",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "253",
number = "0",
pages = "584 - 598",
year = "2013",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2012.06.023",
url = "http://www.sciencedirect.com/science/article/pii/S0045782512002204",
author = "P.B. Bornemann and F. Cirak",
keywords = "Finite elements",
keywords = "Hierarchical b-splines",
keywords = "Subdivision schemes",
keywords = "Isogeometric analysis"
}

@article{daVeiga2012b,
title = "Anisotropic NURBS approximation in isogeometric analysis",
journal = "Computer Methods in Applied Mechanics and Engineering",
volume = "209-212",
number = "0",
pages = "1 - 11",
year = "2012",
note = "",
issn = "0045-7825",
doi = "10.1016/j.cma.2011.10.016",
url = "http://www.sciencedirect.com/science/article/pii/S0045782511003379",
author = "L. Beir{\~a}o da Veiga and D. Cho and G. Sangalli",
keywords = "Isogeometric analysis",
keywords = "Anisotropic refinement",
keywords = "Error estimates"
}

@article{Buffa2013a,
title = "BPX-preconditioning for isogeometric analysis ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "265",
number = "",
pages = "63 - 70",
year = "2013",
note = "",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2013.05.014",
url = "http://www.sciencedirect.com/science/article/pii/S004578251300131X",
author = "Annalisa Buffa and Helmut Harbrecht and Angela Kunoth and Giancarlo Sangalli",
keywords = "Isogeometric analysis",
keywords = "Elliptic PDE",
keywords = "B-splines",
keywords = "Multilevel preconditioning",
keywords = "BPX-preconditioner",
keywords = "Uniformly bounded condition number "
}

@article{Gahalaut2013a,
title = "Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "266",
number = "",
pages = "40 - 56",
year = "2013",
note = "",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2013.07.002",
url = "http://www.sciencedirect.com/science/article/pii/S0045782513001722",
author = "K.P.S. Gahalaut and S.K. Tomar and J.K. Kraus",
keywords = "Isogeometric analysis",
keywords = "B-splines and NURBS",
keywords = "Explicit form of B-splines",
keywords = "AMLI methods",
keywords = "Hierarchical spaces "
}

% ********************************************************************
%                   Functional Analysis
% ********************************************************************
@book{Brezis2011a,
   title = "Functional analysis, Sobolev spaces and partial differential equations",
   author = "Br\'ezis, H.",
   series = "Universitext",
   publisher = "Springer",
   address = "New York, Heidelberg, London",
   url = "http://opac.inria.fr/record=b1134660",
   isbn = "978-0-387-70913-0",
   year = 2011
}

@book{girault1986a,
  title={Finite element methods for Navier-Stokes equations: theory and algorithms},
  author={Girault, V. and Raviart, P.A.},
  isbn={9783540157960},
  lccn={85030387},
  series={Springer series in computational mathematics},
  url={https://books.google.de/books?id=BVfvAAAAMAAJ},
  year={1986},
  publisher={Springer-Verlag}
}

@book{Brezzi1991a,
 author = {Brezzi, Franco and Fortin, Michel},
 title = {Mixed and Hybrid Finite Element Methods},
 year = {1991},
 isbn = {0-387-97582-9},
 publisher = {Springer-Verlag New York, Inc.},
 address = {New York, NY, USA},
} 

@book{tartar2007a,
  title={An Introduction to Sobolev Spaces and Interpolation Spaces},
  author={Tartar, L.},
  isbn={9783540714835},
  series={Lecture Notes of the Unione Matematica Italiana},
  url={https://books.google.de/books?id=pQB1kiz\_vbIC},
  year={2007},
  publisher={Springer}
}
@book{rudin2006a,
  title={Functional Analysis},
  author={Rudin, W.},
  isbn={9780070619883},
  lccn={90005677},
  series={International series in pure and applied mathematics},
  url={https://books.google.de/books?id=l7XFfDmjp5IC},
  year={2006},
  publisher={McGraw-Hill}
}
@book{evans1998a,
  title={Partial Differential Equations},
  author={Evans, L.C.},
  isbn={9780821807729},
  lccn={97041033},
  series={Graduate studies in mathematics},
  url={https://books.google.de/books?id=5Pv4LVB\_m8AC},
  year={1998},
  publisher={American Mathematical Society}
}
@book{yoshida2013a,
  title={Functional Analysis},
  author={Yoshida, K.},
  isbn={9783662257623},
  series={Grundlehren der mathematischen Wissenschaften},
  url={https://books.google.de/books?id=2Mb3CAAAQBAJ},
  year={2013},
  publisher={Springer Berlin Heidelberg}
}

@book{Brezis1999a,
  title={Analyse fonctionnelle: th{\'e}orie et applications},
  author={Br{\'e}zis, H.},
  isbn={9782100043149},
  series={Collection Math{\'e}matiques appliqu{\'e}es pour la ma{\^\i}trise},
  url={https://books.google.de/books?id=aykKPQAACAAJ},
  year={1999},
  publisher={Dunod}
}

@article {Amrouche98a,
author = {Amrouche, C. and Bernardi, C. and Dauge, M. and Girault, V.},
title = {Vector potentials in three-dimensional non-smooth domains},
journal = {Mathematical Methods in the Applied Sciences},
volume = {21},
number = {9},
publisher = {John Wiley & Sons, Ltd},
issn = {1099-1476},
url = {http://dx.doi.org/10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B},
doi = {10.1002/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B},
pages = {823--864},
year = {1998},
}

@book{monk_book,
author = {Monk P.},
title = {Finite Element Methods for Maxwell''s Equations},
year = {2003},
publisher={Calderon Press (Oxford)},
isbn={978-0-19-850888-5},
}

% ********************************************************************
%                              ASP 
% ********************************************************************
@article{Arnold1997a,
    author = {Arnold, Douglas N. and Falk, Richard S. and Winther, R.},
    citeulike-article-id = {9783540},
    journal = {Math. Comp.},
    keywords = {domain\_decomposition, fem, mixed, multigrid},
    mrnumber = {MR1401938 (97i:65177)},
    number = {219},
    pages = {957--984},
    pdf = {http://umn.edu/\~{}arnold/papers/hdiv.pdf},
    posted-at = {2011-09-19 19:08:03},
    priority = {2},
    title = {Preconditioning in {\$H({\\rm div})\$} and applications},
    volume = {66},
    year = {1997}
}

@ARTICLE{Arnold1997b,
    author = {Douglas N. Arnold and Richard S. Falk and Ragnar Winther},
    title = {Multigrid Preconditioning in H(div) on Non-convex Polygons},
    journal = {Comput. and Appl. Math},
    year = {1997},
    volume = {17},
    pages = {303--315}
}

@Article{Arnold2000a,
author="Arnold, N. Douglas
and Falk, S. Richard
and Winther, Ragnar",
title="Multigrid in $H(div)$ and $H(curl)$",
journal="Numerische Mathematik",
year="2000",
volume="85",
number="2",
pages="197--217",
issn="0945-3245",
doi="10.1007/PL00005386",
url="http://dx.doi.org/10.1007/PL00005386"
}

@ARTICLE{Chen2016a,
   author = {{Chen}, L.},
    title = "{Multigrid Methods for Constrained Minimization Problems and Application to Saddle Point Problems}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1601.04091},
 primaryClass = "math.NA",
 keywords = {Mathematics - Numerical Analysis, 65N55, 65F10, 65N22, 65N30},
     year = 2016,
    month = jan,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160104091C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Chen2015a,
title = "An auxiliary space multigrid preconditioner for the weak Galerkin method ",
journal = "Computers \& Mathematics with Applications ",
volume = "70",
number = "4",
pages = "330 - 344",
year = "2015",
note = "",
issn = "0898-1221",
doi = "http://dx.doi.org/10.1016/j.camwa.2015.04.016",
url = "http://www.sciencedirect.com/science/article/pii/S0898122115001972",
author = "Long Chen and Junping Wang and Yanqiu Wang and Xiu Ye",
keywords = "Weak Galerkin finite element methods",
keywords = "Multigrid",
keywords = "Preconditioner "
}

@Article{Grasedyck2015a,
author="Grasedyck, Lars
and Wang, Lu
and Xu, Jinchao",
title="A nearly optimal multigrid method for general unstructured grids",
journal="Numerische Mathematik",
year="2015",
pages="1--30",
issn="0945-3245",
doi="10.1007/s00211-015-0785-7",
url="http://dx.doi.org/10.1007/s00211-015-0785-7"
}

@article{Griebel1995a,
 author = {Griebel, M. and Oswald, P.},
 title = {On the Abstract Theory of Additive and Multiplicative Schwarz Algorithms},
 journal = {Numer. Math.},
 issue_date = {April 1995},
 volume = {70},
 number = {2},
 month = apr,
 year = {1995},
 issn = {0029-599X},
 pages = {163--180},
 numpages = {18},
 url = {http://dx.doi.org/10.1007/s002110050115},
 doi = {10.1007/s002110050115},
 acmid = {218602},
 publisher = {Springer-Verlag New York, Inc.},
 address = {Secaucus, NJ, USA},
}

@article{Hiptmair2007a,
author = {Ralf Hiptmair and Jinchao Xu},
title = {Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces},
journal = {SIAM Journal on Numerical Analysis},
volume = {45},
number = {6},
pages = {2483-2509},
year = {2007},
doi = {10.1137/060660588},
URL = {http://dx.doi.org/10.1137/060660588},
eprint = {http://dx.doi.org/10.1137/060660588}
}

@Article{Hiptmair2006a,
author="Hiptmair, R.
and Widmer, G.
and Zou, J.",
title="Auxiliary space preconditioning in $H_0(curl; \Omega)$",
journal="Numerische Mathematik",
year="2006",
volume="103",
number="3",
pages="435--459",
issn="0945-3245",
doi="10.1007/s00211-006-0683-0",
url="http://dx.doi.org/10.1007/s00211-006-0683-0"
}

@Article{Hiptmair2009a,
    author = {Ralf Hiptmair and W.-Y. Zheng},
    title = {Local multigrid in $H(curl)$},
    journal = {J. Comput. Math.},
    volume = {27},
    number = {5},
    pages = {573--603},
    doi = {http://dx.doi.org/10.4208/jcm.2009.27.5.012},
    issn = {0254-9409 },
    year = {2009}
}

@article{Kolev2009a,
 ISSN = {02549409, 19917139},
 URL = {http://www.jstor.org/stable/43693530},
 author = {Tzanio V. Kolev, Panayot S. Vassilevski},
 journal = {Journal of Computational Mathematics},
 number = {5},
 pages = {604-623},
 publisher = {Institute of Computational Mathematics and Scientific/Engineering Computing},
 title = {PARALLEL AUXILIARY SPACE AMG FOR H(curl) PROBLEMS},
 volume = {27},
 year = {2009}
}

@Inbook{Kolev2008a,
author="Kolev, Tzanio V.
and Vassilevski, Panayot S.",
editor="Langer, Ulrich
and Discacciati, Marco
and Keyes, David E.
and Widlund, Olof B.
and Zulehner, Walter",
title="Auxiliary Space AMG for H(curl) Problems",
bookTitle="Domain Decomposition Methods in Science and Engineering XVII",
year="2008",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="147--154",
isbn="978-3-540-75199-1",
doi="10.1007/978-3-540-75199-1_13",
url="http://dx.doi.org/10.1007/978-3-540-75199-1_13"
}

@Inbook{Kunoth2015a,
author="Kunoth, Angela",
editor="J{\"u}ttler, Bert
and Simeon, Bernd",
title="Multilevel Preconditioning for Variational Problems",
bookTitle="Isogeometric Analysis and Applications 2014",
year="2015",
publisher="Springer International Publishing",
address="Cham",
pages="247--281",
isbn="978-3-319-23315-4",
doi="10.1007/978-3-319-23315-4_11",
url="http://dx.doi.org/10.1007/978-3-319-23315-4_11"
}

@article{Li2015a,
title = "A two-level algorithm for the weak Galerkin discretization of diffusion problems ",
journal = "Journal of Computational and Applied Mathematics ",
volume = "287",
number = "",
pages = "179 - 195",
year = "2015",
note = "",
issn = "0377-0427",
doi = "http://dx.doi.org/10.1016/j.cam.2015.03.043",
url = "http://www.sciencedirect.com/science/article/pii/S037704271500196X",
author = "Binjie Li and Xiaoping Xie",
keywords = "Diffusion problem",
keywords = "Weak Galerkin finite element",
keywords = "Condition number",
keywords = "Two-level algorithm",
keywords = "X–Z identity "
}

@article{Li2016a,
author = {Binjie Li and Xiaoping Xie},
title = {BPX Preconditioner for Nonstandard Finite Element Methods for Diffusion Problems},
journal = {SIAM Journal on Numerical Analysis},
volume = {54},
number = {2},
pages = {1147-1168},
year = {2016},
doi = {10.1137/140999268},
URL = {http://dx.doi.org/10.1137/140999268},
eprint = {http://dx.doi.org/10.1137/140999268}
}

@Inbook{Wang2011a,
author="Wang, Junxian
and Shu, Shi
and Zhong, Liuqiang",
editor="Huang, Yunqing
and Kornhuber, Ralf
and Widlund, Olof
and Xu, Jinchao",
title="Efficient Parallel Preconditioners for High-Order Finite Element Discretizations of H(grad) and H(curl) Problems",
bookTitle="Domain Decomposition Methods in Science and Engineering XIX",
year="2011",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="325--332",
isbn="978-3-642-11304-8",
doi="10.1007/978-3-642-11304-8_37",
url="http://dx.doi.org/10.1007/978-3-642-11304-8_37"
}

@article{Xu1992a,
author = {Jinchao Xu},
title = {Iterative Methods by Space Decomposition and Subspace Correction},
journal = {SIAM Review},
volume = {34},
number = {4},
pages = {581-613},
year = {1992},
doi = {10.1137/1034116},
URL = {http://dx.doi.org/10.1137/1034116},
eprint = {http://dx.doi.org/10.1137/1034116}
}

@Article{Xu1996a,
author="Xu, J.",
title="The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids",
journal="Computing",
year="1996",
volume="56",
number="3",
pages="215--235",
issn="1436-5057",
doi="10.1007/BF02238513",
url="http://dx.doi.org/10.1007/BF02238513"
}

@article{Xu2001a,
title = "The method of subspace corrections ",
journal = "Journal of Computational and Applied Mathematics ",
volume = "128",
number = "1–2",
pages = "335 - 362",
year = "2001",
note = "Numerical Analysis 2000. Vol. VII: Partial Differential Equations ",
issn = "0377-0427",
doi = "http://dx.doi.org/10.1016/S0377-0427(00)00518-5",
url = "http://www.sciencedirect.com/science/article/pii/S0377042700005185",
author = "Jinchao Xu"
}

@Inbook{Xu2009a,
author="Xu, Jinchao
and Chen, Long
and Nochetto, Ricardo H.",
editor="DeVore, Ronald 
and Kunoth, Angela",
title="Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids",
bookTitle="Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday",
year="2009",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="599--659",
isbn="978-3-642-03413-8",
doi="10.1007/978-3-642-03413-8_14",
url="http://dx.doi.org/10.1007/978-3-642-03413-8_14"
}

@article{Xu2002a,
 ISSN = {08940347, 10886834},
 URL = {http://www.jstor.org/stable/827108},
 author = {Jinchao Xu, Ludmil Zikatanov},
 journal = {Journal of the American Mathematical Society},
 number = {3},
 pages = {573-597},
 publisher = {American Mathematical Society},
 title = {The Method of Alternating Projections and the Method of Subspace Corrections in Hilbert Space},
 volume = {15},
 year = {2002}
}

% ********************************************************************
%                             TO SORT 
% ********************************************************************

@article{buffa2011isogeometric,
  title={Isogeometric discrete differential forms in three dimensions},
  author={Buffa, Annalisa and Rivas, Judith and Sangalli, Giancarlo and V{\'a}zquez, Rafael},
  journal={SIAM Journal on Numerical Analysis},
  volume={49},
  number={2},
  pages={818--844},
  year={2011},
  publisher={SIAM}
}

@phdthesis{zhao2004analysis,
  title={Analysis of finite element approximation and iterative methods for time-dependent Maxwell problems},
  author={Zhao, Jun},
  year={2004},
  school={Texas A\&M University}
}

@article{pasciak2002overlapping,
  title={Overlapping Schwarz methods in H(curl) on nonconvex domains, East-West J},
  author={Pasciak, J and Zhao, J},
  journal={Numer. Anal},
  volume={10},
  pages={221--234},
  year={2002}
}

@book{PieglBook1996,
  title={The NURBS book},
  author={Piegl, Les and Tiller, Wayne},
  year={1996},
  publisher={Springer Science \& Business Media}
}

@book{schumaker2007spline,
  title={Spline functions: basic theory},
  author={Schumaker, Larry},
  year={2007},
  publisher={Cambridge University Press}
}

@book{rogers2001introduction,
  title={An introduction to NURBS: with historical perspective},
  author={Rogers, David F},
  year={2001},
  publisher={Morgan Kaufmann}
}

@book{prautzsch2002bezier,
  title={B{\'e}zier and B-spline techniques},
  author={Prautzsch, Hartmut and Boehm, Wolfgang and Paluszny, Marco},
  year={2002},
  publisher={Springer Science \& Business Media}
}

@book{gu2008computational,
  title={Computational conformal geometry},
  author={Gu, Xianfeng David and Yau, Shing-Tung},
  volume={1},
  year={2008},
  publisher={International Press Somerville, MA}
}

@book{farin2002curves,
  title={Curves and surfaces for CAGD: a practical guide},
  author={Farin, Gerald E and Farin, Gerald},
  year={2002},
  publisher={Morgan Kaufmann}
}

@book{farin1999nurbs,
  title={NURBS for Curve \& Surface Design: From Projective Geometry to Practical Use},
  author={Farin, Gerald},
  year={1999},
  publisher={CRC Press}
}

@book{cohen2001geometric,
  title={Geometric modeling with splines: an introduction},
  author={Cohen, Elaine and Riesenfeld, Richard F and Elber, Gershon},
  year={2001},
  publisher={CRC Press}
}

@article{hiptmair2007nodal,
  title={Nodal auxiliary space preconditioning in H (curl) and H (div) spaces},
  author={Hiptmair, Ralf and Xu, Jinchao},
  journal={SIAM Journal on Numerical Analysis},
  volume={45},
  number={6},
  pages={2483--2509},
  year={2007},
  publisher={SIAM}
}

@book{adams2003sobolev,
  title={Sobolev spaces},
  author={Adams, Robert A and Fournier, John JF},
  year={2003},
  publisher={Elsevier}
}

@book{monk2003finite,
  title={Finite element methods for Maxwell's equations},
  author={Monk, Peter and others},
  year={2003},
  publisher={Oxford University Press}
}

@book{girault2012finite,
  title={Finite element methods for Navier-Stokes equations: theory and algorithms},
  author={Girault, Vivette and Raviart, Pierre-Arnaud},
  volume={5},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@incollection{kolev2008auxiliary,
  title={Auxiliary space AMG for H (curl) problems},
  author={Kolev, Tzanio V and Vassilevski, Panayot S},
  booktitle={Domain decomposition methods in science and engineering XVII},
  pages={147--154},
  year={2008},
  publisher={Springer}
}


@article{kolev2009parallel,
  title={Parallel auxiliary space AMG for H (curl) problems},
  author={Kolev, Tzanio V and Vassilevski, Panayot S},
  journal={Journal of Computational Mathematics},
  pages={604--623},
  year={2009},
  publisher={JSTOR}
}

@article{chen2015auxiliary,
  title={An auxiliary space multigrid preconditioner for the weak Galerkin method},
  author={Chen, Long and Wang, Junping and Wang, Yanqiu and Ye, Xiu},
  journal={Computers \& Mathematics with Applications},
  volume={70},
  number={4},
  pages={330--344},
  year={2015},
  publisher={Elsevier}
}

@article{hiptmair2006auxiliary,
  title={Auxiliary space preconditioning in H 0 (curl; $\Omega$)},
  author={Hiptmair, Ralf and Widmer, Gisela and Zou, Jun},
  journal={Numerische Mathematik},
  volume={103},
  number={3},
  pages={435--459},
  year={2006},
  publisher={Springer}
}

@article{xu1992iterative,
  title={Iterative methods by space decomposition and subspace correction},
  author={Xu, Jinchao},
  journal={SIAM review},
  volume={34},
  number={4},
  pages={581--613},
  year={1992},
  publisher={SIAM}
}

@book{nepomnyaschikh1991decomposition,
  title={Decomposition and fictitious domains methods for elliptic boundary value problems},
  author={Nepomnyaschikh, SV},
  year={1991},
  publisher={Citeseer}
}

@article{bazilevs2006isogeometric,
  title={Isogeometric analysis: approximation, stability and error estimates for h-refined meshes},
  author={Bazilevs, Yuri and Beirao da Veiga, L and Cottrell, J Austin and Hughes, Thomas JR and Sangalli, Giancarlo},
  journal={Mathematical Models and Methods in Applied Sciences},
  volume={16},
  number={07},
  pages={1031--1090},
  year={2006},
  publisher={World Scientific}
}

@article{da2014mathematical,
  title={Mathematical analysis of variational isogeometric methods},
  author={Da Veiga, L Beirao and Buffa, Annalisa and Sangalli, Giancarlo and V{\'a}zquez, Rafael},
  journal={Acta Numerica},
  volume={23},
  pages={157},
  year={2014},
  publisher={Cambridge University Press}
}

@article{hughes2005isogeometric,
  title={Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement},
  author={Hughes, Thomas JR and Cottrell, John A and Bazilevs, Yuri},
  journal={Computer methods in applied mechanics and engineering},
  volume={194},
  number={39-41},
  pages={4135--4195},
  year={2005},
  publisher={Elsevier}
}

@book{cottrell2009isogeometric,
  title={Isogeometric analysis: toward integration of CAD and FEA},
  author={Cottrell, J Austin and Hughes, Thomas JR and Bazilevs, Yuri},
  year={2009},
  publisher={John Wiley \& Sons}
}

@article{mazza2019,
  title={Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions},
  author={Mazza, Mariarosa and Ratnani, Ahmed and Serra-Capizzano, Stafano},
  journal={Mathematics of Computation},
  volume={88},
  pages={1155-1188},
  year={2019},
  publisher={American Mathematical Society}
}

@article{garoni2014,
  author="Garoni, Carlo
  and Manni, Carla
  and Pelosi, Francesca
  and Serra-Capizzano, Stefano
  and Speleers, Hendrik",
  title="On the spectrum of stiffness matrices arising from isogeometric analysis",
  journal="Numerische Mathematik",
  year="2014",
  volume="127",
  number="4",
  pages="751--799",
  issn="0945-3245",
  doi="10.1007/s00211-013-0600-2",
  url="http://dx.doi.org/10.1007/s00211-013-0600-2"
}


@article{sangalli2016,
  author = {Sangalli, Giancarlo and Tani, Mattia},
  title = {Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation},
  journal = {SIAM Journal on Scientific Computing},
  volume = {38},
  number = {6},
  pages = {A3644-A3671},
  year = {2016},
  doi = {10.1137/16M1062788},
}

@article{lynch1964,
  author = {Lynch, R.E. and Rice, J.R. and Thomas, D.H.},
  title = {Direct solution of partial difference equations by tensor product methods},
  journal = {Numerische Mathematik},
  volume = {6},
  pages = {185-199},
  year = {1964},
  doi = {10.1007/BF01386067},
}

@book{Bernstein_book,
  title={Matrix Mathematics: Theory, Facts, and Formulas},
  author={Bernstein D. S.},
  publisher={PRINCETON UNIVERSITY PRESS},
  isbn={978-0-691-13287-7},
  year={2009},
  edition={second}
}


@book{Graham_book,
author = {A. Graham},
title = {Kronecker products and matrix calculus with applications},
year = {1981},
masid = {1343202}
}

@article{vanloan2000,
 author = {van Loan, Charles F.},
 title = {The ubiquitous Kronecker product},
 journal = {J. Comput. Appl. Math.},
 volume = {123},
 issue = {1-2},
 month = {November},
 year = {2000},
 issn = {0377-0427},
 pages = {85--100},
 numpages = {16},
 url = {http://portal.acm.org/citation.cfm?id=363882.363888},
 doi = {10.1016/S0377-0427(00)00393-9},
 acmid = {363888},
 publisher = {Elsevier Science Publishers B. V.},
 address = {Amsterdam, The Netherlands, The Netherlands},
} 

@article{MARSDEN19707,
title = "An identity for spline functions with applications to variation-diminishing spline approximation",
journal = "Journal of Approximation Theory",
volume = "3",
number = "1",
pages = "7 - 49",
year = "1970",
issn = "0021-9045",
doi = "https://doi.org/10.1016/0021-9045(70)90058-4",
url = "http://www.sciencedirect.com/science/article/pii/0021904570900584",
author = "Martin J Marsden"
}

@article{DEBOOR197319,
title = {Spline approximation by quasiinterpolants},
journal = {Journal of Approximation Theory},
volume = {8},
number = {1},
pages = {19-45},
year = {1973},
issn = {0021-9045},
doi = {https://doi.org/10.1016/0021-9045(73)90029-4},
url = {https://www.sciencedirect.com/science/article/pii/0021904573900294},
author = {C {de Boor} and G.J Fix}
}

@article{FAROUKI1987191,
title = {On the numerical condition of polynomials in Bernstein form},
journal = {Computer Aided Geometric Design},
volume = {4},
number = {3},
pages = {191-216},
year = {1987},
issn = {0167-8396},
doi = {https://doi.org/10.1016/0167-8396(87)90012-4},
url = {https://www.sciencedirect.com/science/article/pii/0167839687900124},
author = {R.T. Farouki and V.T. Rajan},
keywords = {Condition numbers, polynomial roots, Bernstein basis},
}


@article{FAROUKI19881,
title = {Algorithms for polynomials in Bernstein form},
journal = {Computer Aided Geometric Design},
volume = {5},
number = {1},
pages = {1-26},
year = {1988},
issn = {0167-8396},
doi = {https://doi.org/10.1016/0167-8396(88)90016-7},
url = {https://www.sciencedirect.com/science/article/pii/0167839688900167},
author = {R.T. Farouki and V.T. Rajan},
keywords = {Polynomial algorithms, condition numbers, Berstein basis},
}

@article{DEBOOR2005,
title = {Divided Differences},
journal = {Surveys in Approximation Theory},
volume = {1},
pages = {46-69},
year = {2005},
url = {https://www.emis.de/journals/SAT/papers/2/},
author = {C {de Boor}}
}

@article{Roozegar2013,
title = {a concise formula for two dimensional divided differences with multiple knots.},
journal = {Journal of Mathematical Extension},
volume = {7},
pages = {63-69},
year = {2013},
url = {https://www.sid.ir/en/journal/ViewPaper.aspx?id=364757},
author = {Roozegar, R., and Jafari, A.}
}

@book{bezhaev2013variational,
  title={Variational Theory of Splines},
  author={Bezhaev, A.Y. and Vasilenko, V.A.},
  isbn={9781475734287},
  url={https://books.google.co.ma/books?id=luvvBwAAQBAJ},
  year={2013},
  publisher={Springer US}
}

@article{Werner1984,
 ISSN = {00255718, 10886842},
 URL = {http://www.jstor.org/stable/2007406},
 abstract = {We show that the Lagrangian form of the interpolating polynomial can be calculated with the same number of arithmetic operations as the Newtonian form.},
 author = {Wilhelm Werner},
 journal = {Mathematics of Computation},
 number = {167},
 pages = {205--217},
 publisher = {American Mathematical Society},
 title = {Polynomial Interpolation: Lagrange versus Newton},
 volume = {43},
 year = {1984}
}

@article{LYCHE1975294,
title = {Local spline approximation methods},
journal = {Journal of Approximation Theory},
volume = {15},
number = {4},
pages = {294-325},
year = {1975},
issn = {0021-9045},
doi = {https://doi.org/10.1016/0021-9045(75)90091-X},
url = {https://www.sciencedirect.com/science/article/pii/002190457590091X},
author = {Tom Lyche and Larry L Schumaker}
}

@article{Barry1996deBD,
  title={de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves},
  author={Phillip J. Barry},
  journal={Constructive Approximation},
  year={1996},
  volume={12},
  pages={385-408}
}

@inproceedings{Boor1972OnCW,
  title={On Calculating with Mplines},
  author={C. D. Boor},
  year={1972}
}


@book{devore1993constructive,
  title={Constructive Approximation},
  author={DeVore, R.A. and Lorentz, G.G.},
  isbn={9783540506270},
  lccn={lc93018420},
  series={Grundlehren der mathematischen Wissenschaften},
  url={https://books.google.co.ma/books?id=cDqNW6k7\_ZwC},
  year={1993},
  publisher={Springer Berlin Heidelberg}
}

@article{Boldo2004,
  title={A Simple Test Qualifying the Accuracy of Horner'S Rule for Polynomials},
  author={Sylvie Boldo and Marc Daumas},
  journal={Numerical Algorithms},
  year={2004},
  volume={37},
  pages={45-60}
}

@article{Speleers2017,
author = {Speleers, Hendrik},
title = {Hierarchical Spline Spaces: Quasi-Interpolants and Local Approximation Estimates},
year = {2017},
issue_date = {April     2017},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
volume = {43},
number = {2},
issn = {1019-7168},
url = {https://doi.org/10.1007/s10444-016-9483-y},
doi = {10.1007/s10444-016-9483-y},
journal = {Adv. Comput. Math.},
month = apr,
pages = {235-255},
numpages = {21},
keywords = {65D17, Tensor-product B-splines, 41A15, Local refinement, Quasi-interpolation, Local approximation, Hierarchical bases, 65D07}
}

@book{HighamBook2002,
author = {Higham, Nicholas J.},
title = {Accuracy and Stability of Numerical Algorithms},
publisher = {Society for Industrial and Applied Mathematics},
year = {2002},
doi = {10.1137/1.9780898718027},
address = {},
edition   = {Second},
URL = {https://epubs.siam.org/doi/abs/10.1137/1.9780898718027},
eprint = {https://epubs.siam.org/doi/pdf/10.1137/1.9780898718027}
}


@book{goldman_lyche_book,
author = {Goldman, Ronald N. and Lyche, Tom},editor = {Ronald N. Goldman and Tom Lyche},
title = {Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces},
publisher = {Society for Industrial and Applied Mathematics},
year = {1992},
doi = {10.1137/1.9781611971583},
address = {Philadelphia, PA},
edition   = {},
URL = {https://epubs.siam.org/doi/abs/10.1137/1.9781611971583},
eprint = {https://epubs.siam.org/doi/pdf/10.1137/1.9781611971583}
}

@article{Huang2005FastDE,
  title={Fast degree elevation and knot insertion for B-spline curves},
  author={Qixing Huang and Shimin Hu and Ralph Robert Martin},
  journal={Comput. Aided Geom. Des.},
  year={2005},
  volume={22},
  pages={183-197}
}

@book{BoffiBook2013,
  title={Mixed Finite Element Methods and Applications},
  author={Boffi, D. and Brezzi, F. and Fortin, M.},
  isbn={9783642365195},
  lccn={2013940257},
  series={Springer Series in Computational Mathematics},
  url={https://books.google.co.ma/books?id=mRhAAAAAQBAJ},
  year={2013},
  publisher={Springer Berlin Heidelberg}
}



@article{bathe1976finite,
  title={Finite Element Procedures in Engineering Analysis},
  author={Bathe, Klaus-J{\"u}rgen},
  journal={Journal of Engineering Mechanics},
  year={1976},
}

@book{hughes1987finite,
  title={The Finite Element Method: Linear Static and Dynamic Finite Element Analysis},
  author={Hughes, Thomas JR},
  year={1987},
  publisher={Dover Publications},
}

@book{cook2001concepts,
  title={Concepts and Applications of Finite Element Analysis},
  author={Cook, Robert D and Malkus, David S and Plesha, Michael E},
  year={2001},
  publisher={Wiley},
}

@article{hughes1979multidimensional,
  title={A multidimensional upwind scheme with no crosswind diffusion},
  author={Hughes, Thomas JR and Brooks, AN},
  journal={Computer Methods in Applied Mechanics and Engineering},
  year={1979},
}

@book{versteeg2007introduction,
  title={An Introduction to Computational Fluid Dynamics: The Finite Volume Method},
  author={Versteeg, Henk K and Malalasekera, Wanessa},
  year={2007},
  publisher={Pearson Education},
}

@book{jin2002finite,
  title={The Finite Element Method in Electromagnetics},
  author={Jin, Jianming},
  year={2002},
  publisher={Wiley},
}

@book{cowin2007bone,
  title={Bone Mechanics Handbook},
  author={Cowin, Stephen C},
  year={2007},
  publisher={CRC Press},
}

@book{elmer2010introduction,
  title={Introduction to Nuclear Engineering},
  author={Elmer, John W},
  year={2010},
  publisher={CRC Press},
}

@book{bear1972dynamics,
  title={Dynamics of Fluids in Porous Media},
  author={Bear, Jacob},
  year={1972},
  publisher={American Elsevier Publishing Company},
}

@book{duffie2013solar,
  title={Solar Engineering of Thermal Processes},
  author={Duffie, John A and Beckman, William A},
  year={2013},
  publisher={Wiley},
}

@book{lay1995modern,
  title={Modern Global Seismology},
  author={Lay, Thorne and Wallace, Terry C},
  year={1995},
  publisher={Academic Press},
}

@book{bird2007transport,
  title={Transport Phenomena},
  author={Bird, Robert B and Stewart, Warren E and Lightfoot, Edwin N},
  year={2007},
  publisher={Wiley},
}

@book{zienkiewicz1971finite,
  title={The Finite Element Method in Engineering Science},
  author={Zienkiewicz, Olgierd C},
  journal={Proceedings of the Royal Society A},
  year={1971},
}

@book{viceconti2008virtual,
  title={The Virtual Physiological Human: A European Initiative for Integrative Biomedical Modelling},
  author={Viceconti, Marco and Clapworthy, Gordon and Van Sint Jan, Serge},
  booktitle={Studies in Health Technology and Informatics},
  year={2008},
}



@article{schmidt2011magnetohydrodynamics,
  title={Magnetohydrodynamics: historical evolution and trends},
  author={Schmidt, Hartmut},
  journal={Plasma Physics and Controlled Fusion},
  volume={53},
  number={12},
  pages={124002},
  year={2011},
}

@book{davidson2001introduction,
  title={An Introduction to Magnetohydrodynamics},
  author={Davidson, Peter A},
  year={2001},
  publisher={Cambridge University Press},
}

@article{bellan2006fundamentals,
  title={Fundamentals of Plasma Physics},
  author={Bellan, Paul M},
  journal={Cambridge University Press},
  year={2006},
}

@article{roberts1992introduction,
  title={An Introduction to Magnetohydrodynamics},
  author={Roberts, Peter H},
  journal={Longman Scientific \& Technical},
  year={1992},
}




@book{Zienkiewicz2005,
  author    = {O. C. Zienkiewicz and J. Z. Zhu and R. L. Taylor},
  title     = {The Finite Element Method: Its Basis and Fundamentals},
  publisher = {Elsevier},
  year      = {2005}
}

@book{Ainsworth2000,
  author    = {M. Ainsworth and J. T. Oden},
  title     = {A Posteriori Error Estimation in Finite Element Analysis},
  publisher = {John Wiley \& Sons},
  year      = {2000}
}

@book{Cottrell2009,
  author    = {J. A. Cottrell and T. J. Hughes and Y. Bazilevs},
  title     = {Isogeometric Analysis: Toward Integration of CAD and FEA},
  publisher = {John Wiley \& Sons},
  year      = {2009}
}

@article{Stevenson2017,
  author  = {R. Stevenson and J. Thomas},
  title   = {A Posteriori Error Estimation Techniques in Isogeometric Analysis},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume  = {312},
  pages   = {436--463},
  year    = {2017}
}

@article{Babuska2001,
  author  = {I. Babuška and T. Strouboulis},
  title   = {The Finite Element Method and Its Reliability},
  journal = {Numerische Mathematik},
  volume  = {88},
  number  = {4},
  pages   = {747--776},
  year    = {2001}
}

@book{Bangerth2003,
  author    = {W. Bangerth and R. Rannacher},
  title     = {Adaptive Finite Element Methods for Differential Equations},
  publisher = {Birkhäuser},
  year      = {2003}
}

@article{Buffa2011,
  author  = {A. Buffa and G. Sangalli and R. Vázquez},
  title   = {Isogeometric Analysis in Electromagnetics: B-splines Approximation},
  journal = {Computer Methods in Applied Mechanics and Engineering},
  volume  = {200},
  number  = {9-12},
  pages   = {1240--1252},
  year    = {2011}
}



@article{Villani2003,
  author    = {Cédric Villani},
  title     = {Topics in Optimal Transportation},
  journal   = {American Mathematical Society},
  year      = {2003}
}

@book{Ambrosio2008,
  author    = {Luigi Ambrosio and Nicola Gigli and Giuseppe Savaré},
  title     = {Gradient Flows in Metric Spaces and in the Space of Probability Measures},
  publisher = {Birkhäuser},
  year      = {2008}
}

@article{Cuturi2013,
  author    = {Marco Cuturi},
  title     = {Sinkhorn Distances: Lightspeed Computation of Optimal Transport},
  journal   = {Advances in Neural Information Processing Systems},
  volume    = {26},
  year      = {2013}
}

@article{Brenier1991,
  author    = {Yann Brenier},
  title     = {Polar factorization and monotone rearrangement of vector-valued functions},
  journal   = {Communications on Pure and Applied Mathematics},
  volume    = {44},
  number    = {4},
  pages     = {375--417},
  year      = {1991}
}

@article{Benamou2015,
  author    = {Jean-David Benamou and Guillaume Carlier and Marco Cuturi and Luca Nenna and Gabriel Peyré and Filippo Santambrogio},
  title     = {Iterative Bregman Projections for Regularized Transportation Problems},
  journal   = {SIAM Journal on Scientific Computing},
  volume    = {37},
  number    = {2},
  pages     = {A1111--A1138},
  year      = {2015}
}

@article{Kang2017,
  author    = {Ming Kang and Lin Lin and Lexing Ying},
  title     = {Solving optimal transport problems with Laplacian regularization over graphs},
  journal   = {Journal of Machine Learning Research},
  volume    = {18},
  number    = {1},
  pages     = {1814--1851},
  year      = {2017}
}

@book{Quarteroni2008,
  author    = {Alfio Quarteroni and Riccardo Sacco and Fausto Saleri},
  title     = {Numerical Mathematics},
  publisher = {Springer},
  year      = {2008}
}



@book{jin2015finite,
  title={The Finite Element Method in Electromagnetics},
  author={Jin, Jian-Ming},
  year={2015},
  publisher={Wiley}
}

@article{bossavit1998whitney,
  title={Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism},
  author={Bossavit, Alain},
  journal={IEE Proceedings-A-Science, Measurement and Technology},
  volume={135},
  number={6},
  pages={493--500},
  year={1998},
  publisher={IET}
}

@book{monk2003finite,
  title={Finite element methods for Maxwell's equations},
  author={Monk, Peter},
  year={2003},
  publisher={Oxford University Press}
}



@book{hughes2012finite,
  title={Finite Element Method: A Practical Course},
  author={Hughes, Thomas JR},
  year={2012},
  publisher={CRC Press}
}

@book{donea2003finite,
  title={Finite Element Methods for Flow Problems},
  author={Donea, Jean and Huerta, Antonio},
  year={2003},
  publisher={John Wiley \& Sons}
}

@book{quarteroni2008numerical,
  title={Numerical Models for Differential Problems},
  author={Quarteroni, Alfio and Saleri, Fausto},
  year={2008},
  publisher={Springer}
}



@article{hron2006fluid,
  title={A fluid--structure interaction problem: Existence of solutions and their numerical approximation},
  author={Hron, Jaroslav and Turek, Stefan and Wohlmuth, Barbara I},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={195},
  number={44-47},
  pages={5733--5752},
  year={2006},
  publisher={Elsevier}
}

@book{bathe2014finite,
  title={Finite Element Procedures},
  author={Bathe, Klaus-J{\"u}rgen},
  year={2014},
  publisher={KJ Bathe}
}

@book{quarteroni2017fluid,
  title={Fluid-Structure Interaction: Modelling, Simulation, Optimization},
  author={Quarteroni, Alfio and Formaggia, Luca and Veneziani, Alessandro},
  year={2017},
  publisher={Springer}
}



@book{kirk2004optimal,
  title={Optimal Control Theory: An Introduction},
  author={Kirk, Donald E},
  year={2004},
  publisher={Dover Publications}
}

@book{betts2010practical,
  title={Practical Methods for Optimal Control and Estimation Using Nonlinear Programming},
  author={Betts, John T},
  year={2010},
  publisher={SIAM}
}

@article{triggiani2005optimal,
  title={Optimal regularity, optimal controllability and exact controllability for first order abstract evolution equations},
  author={Triggiani, Roberto},
  journal={In ESAIM: Control, Optimisation and Calculus of Variations},
  volume={11},
  pages={342--365},
  year={2005},
  publisher={EDP Sciences}
}



@article{lasry2007mean,
  title={Mean field games},
  author={Lasry, Jean-Michel and Lions, Pierre-Louis},
  journal={Japanese Journal of Mathematics},
  volume={2},
  number={1},
  pages={229--260},
  year={2007},
  publisher={Springer}
}

@article{huang2018finite,
  title={Finite element approximation of mean-field games},
  author={Huang, Minyi and Malham{\'e}, Roland P and Caines, Peter E},
  journal={Journal of Scientific Computing},
  volume={76},
  number={1},
  pages={143--180},
  year={2018},
  publisher={Springer}
}

@book{cardaliaguet2018notes,
  title={Notes on mean field games},
  author={Cardaliaguet, Pierre},
  year={2018},
  publisher={Springer}
}



@article{Allaire2004,
  author = {Allaire, G. and Jouve, F. and Toader, A. M.},
  title = {Structural optimization using sensitivity analysis and a level-set method},
  journal = {Journal of Computational Physics},
  year = {2004},
  volume = {194},
  number = {1},
  pages = {363-393},
}

@book{Biegler2010,
  author = {Biegler, L. T.},
  title = {Introduction to Advanced Topics of PDE-Constrained Optimization},
  year = {2010},
  publisher = {Springer},
}

@book{Quarteroni2000,
  author = {Quarteroni, A. and Sacco, R. and Saleri, F.},
  title = {Numerical Mathematics},
  year = {2000},
  publisher = {Springer},
}

@article{Schulz2005,
  author = {Schulz, V. H.},
  title = {Lagrange-multiplier-type space decomposition for PDE-constrained optimization},
  journal = {Computational Optimization and Applications},
  year = {2005},
  volume = {31},
  number = {2},
  pages = {189-207},
}

@article{Zolesio1996,
  author = {Zolesio, J. P.},
  title = {Shape sensitivity analysis of systems governed by PDE},
  journal = {Control and Cybernetics},
  year = {1996},
  volume = {25},
  number = {4},
  pages = {579-602},
}

@article{Haasdonk2004,
  author = {Haasdonk, B. and Burkhardt, H.},
  title = {Variational principles for modeling the mechanical behavior of solids: Application to the isotropic case},
  journal = {International Journal for Numerical Methods in Engineering},
  year = {2004},
  volume = {61},
  number = {12},
  pages = {2045-2076},
}

@book{Quarteroni1997,
  author = {Quarteroni, A. and Valli, A.},
  title = {Domain Decomposition Methods for Partial Differential Equations},
  year = {1997},
  publisher = {Oxford University Press},
}

@book{Troltzsch2010,
  author = {Troltzsch, F.},
  title = {Optimal Control of Partial Differential Equations: Theory, Methods, and Applications},
  year = {2010},
  publisher = {American Mathematical Society},
}

@book{Gill1981,
  author = {Gill, P. E. and Murray, W. and Wright, M. H.},
  title = {Practical optimization},
  year = {1981},
  publisher = {Academic Press},
}

@article{Oberkampf2002,
  author = {Oberkampf, W. L. and Trucano, T. G.},
  title = {Verification and validation in computational fluid dynamics},
  journal = {Progress in Aerospace Sciences},
  year = {2002},
  volume = {38},
  number = {3},
  pages = {209-272},
}

@book{Logg2012,
  author = {Logg, A. and Mardal, K. A. and Wells, G. N.},
  title = {Automated Solution of Differential Equations by the Finite Element Method},
  year = {2012},
  publisher = {Springer},
}




@article{strang1977vandermonde,
  author = {Strang, Gilbert and Moler, Cleve and Reinsch, George W.},
  title = {Vandermonde Matrices},
  journal = {SIAM Review},
  year = {1977},
  volume = {19},
  number = {1},
  pages = {1--17},
  doi = {10.1137/1019001},
}

@book{higham2002accuracy,
  author = {Higham, Nicholas J.},
  title = {Accuracy and Stability of Numerical Algorithms},
  year = {2002},
  publisher = {SIAM},
}

@book{golub2013matrix,
  author = {Golub, G. H. and Van Loan, C. F.},
  title = {Matrix Computations},
  year = {2013},
  publisher = {Johns Hopkins University Press},
}

@book{dahlquist2008numerical,
  author = {Dahlquist, Germund and Björck, Åke},
  title = {Numerical Methods},
  year = {2008},
  publisher = {Prentice Hall},
}


@book{karlin1966tchebycheff,
  title={Tchebycheff Systems: With Applications in Analysis and Statistics},
  author={Karlin, Samuel and Studden, William J.},
  year={1966},
  publisher={Wiley}
}


@book{borwein1995polynomials,
  title={Polynomials and Polynomial Inequalities},
  author={Borwein, Peter and Erdelyi, Tamas},
  year={1995},
  publisher={Springer}
}


@book{lorentz1986approximation,
  title={Approximation of Functions},
  author={Lorentz, George G.},
  year={1986},
  publisher={Chelsea Pub Co}
}