references.bib

@book{Langtangen_Mardal_FEM_2019,
  author    = {Langtangen, Hans Petter
and Mardal, Kent-Andre},
  title     = {Introduction to Numerical Methods for Variational Problems},
  year      = {2019},
  publisher = {Springer International Publishing},
  address   = {Cham},
  isbn      = {978-3-030-23788-2},
  doi       = {10.1007/978-3-030-23788-2_1}
}

@article{ufl2014,
  author     = {Aln\ae{}s, Martin S. and Logg, Anders and \O{}lgaard, Kristian B. and Rognes, Marie E. and Wells, Garth N.},
  title      = {Unified Form Language: A Domain-Specific Language for Weak Formulations of Partial Differential Equations},
  year       = {2014},
  issue_date = {February 2014},
  publisher  = {Association for Computing Machinery},
  address    = {New York, NY, USA},
  volume     = {40},
  number     = {2},
  issn       = {0098-3500},
  doi        = {10.1145/2566630},
  journal    = {ACM Trans. Math. Softw.},
  articleno  = {9},
  numpages   = {37}
}

@article{chorin1968numerical,
  author  = {Chorin, Alexandre Joel},
  doi     = {10.1090/S0025-5718-1968-0242392-2},
  journal = {Mathematics of Computation},
  number  = {104},
  pages   = {745--762},
  title   = {{Numerical solution of the Navier-Stokes equations}},
  volume  = {22},
  year    = {1968}
}


@article{Temam1969,
  author    = {Temam, Roger},
  doi       = {10.1007/BF00247696},
  journal   = {Archive for Rational Mechanics and Analysis},
  number    = {2},
  pages     = {135--153},
  publisher = {Springer},
  timestamp = {2019.08.05},
  title     = {{Sur l'approximation de la solution des {\'e}quations de Navier-Stokes par la m{\'e}thode des pas fractionnaires (I)}},
  volume    = {32},
  year      = {1969}
}



@article{goda1979multistep,
  abstract  = {A numerical algorithm for solving two- or three-dimensional incompressible viscous Navier-Stokes equations is presented. The technique presented here is based on a simple variant of the Chorin method and is related to the MAC method. Auxiliary velocity fields are introduced, which are calculated by the use of a fractional-step procedure for the convective and diffusive part of the solution. For the pressure resolution, a triple sweep is used to obtain the fluid pressure. By these fractional techniques, the three-dimensional equations are separated into only one-dimensional forms. Thus, this saves more computation time and makes algorithm simple. Some numerical computations are made on flows within square and cubic cavities, and some comparisons are made in regard to boundary effects in three-dimensional flows. Further, some discussions are made on primary and secondary eddies generated in a cubic cavity, and comparisons with those in a square cavity are also made. It was found that boundary effects mainly locate near a side wall, but these are not negligibly small in a central region in a cubic cavity.},
  author    = {Goda, Katuhiko},
  doi       = {10.1016/0021-9991(79)90088-3},
  issn      = {0021-9991},
  journal   = {Journal of computational physics},
  number    = {1},
  pages     = {76--95},
  publisher = {Elsevier},
  title     = {{A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows}},
  volume    = {30},
  year      = {1979}
}



@book{QuarteroniSaccoSaleri2010,
  title     = {Numerical mathematics},
  publisher = {Springer Science \& Business Media},
  year      = {2010},
  author    = {Quarteroni, Alfio and Sacco, Riccardo and Saleri, Fausto},
  volume    = {37},
  owner     = {andre},
  timestamp = {2019.06.24},
  doi       = {10.1007/b98885}
}

@article{Guermond1999,
  author    = {Guermond, Jean-Luc},
  journal   = {ESAIM: Mathematical Modelling and Numerical Analysis},
  title     = {{Un r{\'e}sultat de convergence d'ordre deux en temps pour l'approximation des {\'e}quations de Navier--Stokes par une technique de projection incr{\'e}mentale}},
  year      = {1999},
  number    = {1},
  pages     = {169--189},
  volume    = {33},
  publisher = {EDP Sciences},
  timestamp = {2020.04.19},
  doi       = {10.1051/m2an:1999101}
}


@book{Langtangen2016,
  author    = {Langtangen, Hans Petter},
  title     = {A Primer on Scientific Programming with Python},
  year      = {2016},
  publisher = {Springer Berlin Heidelberg},
  address   = {Berlin, Heidelberg},
  pages     = {1--49},
  isbn      = {978-3-662-49887-3},
  doi       = {10.1007/978-3-662-49887-3}
}

@book{FenicsTutorial,
  author    = {Langtangen, Hans Petter and Logg, Anders},
  title     = {Solving PDEs in Python: The FEniCS Tutorial I},
  year      = {2016},
  publisher = {Springer International Publishing},
  address   = {Cham},
  pages     = {3--10},
  isbn      = {978-3-319-52462-7},
  doi       = {10.1007/978-3-319-52462-7}
}

@inbook{Langtangen2016scaling,
  author    = {Langtangen, Hans Petter and Pedersen, Geir K.},
  title     = {Advanced partial differential equation models},
  booktitle = {Scaling of Differential Equations},
  year      = {2016},
  publisher = {Springer International Publishing},
  address   = {Cham},
  pages     = {99--134},
  isbn      = {978-3-319-32726-6},
  doi       = {10.1007/978-3-319-32726-6_4}
}


@article{Nitsche1971,
  author  = {Nitsche, J.},
  title   = {{\"U}ber ein Variationsprinzip zur L{\"o}sung von Dirichlet-Problemen bei Verwendung von Teilr{\"a}umen, die keinen Randbedingungen unterworfen sind},
  journal = {Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  year    = {1971},
  month   = {Jul},
  day     = {01},
  volume  = {36},
  number  = {1},
  pages   = {9-15},
  issn    = {1865-8784},
  doi     = {10.1007/BF02995904}
}