dGThermoPoroElasticity_Convergence.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "dGThermoPoroElasticity.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qEKhqU-SIP23"
      },
      "source": [
        "# Thermo-poro-elasticity problems"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i7Hj6-Kz3n0P"
      },
      "source": [
        "We design a discontinuos Galerkin method for solving the linear **thermo-poro-elasticity** problem described by the following set of the equations:\n",
        "\n",
        "$$\n",
        "    \\begin{aligned}\n",
        "-\\boldsymbol\\nabla\\cdot(2\\mu\\boldsymbol\\nabla_s\\boldsymbol{u} + (\\lambda\\boldsymbol\\nabla\\cdot\\boldsymbol{u}-\\alpha p -\\beta T)\\mathbb{I}_d) &= \\boldsymbol{f}, \\quad\\text{in}\\; \\Omega, \\\\\n",
        "\\partial_t(a_0 T - b_0 p + \\beta\\boldsymbol\\nabla\\cdot\\boldsymbol{u}) -\\boldsymbol\\nabla\\cdot(\\Theta\\boldsymbol\\nabla T) &= h, \\quad\\text{in}\\; \\Omega, \\\\\n",
        "\\partial_t(c_0 p - b_0 T + \\alpha\\boldsymbol\\nabla\\cdot\\boldsymbol{u}) -\\boldsymbol\\nabla\\cdot(\\kappa\\boldsymbol\\nabla p) &= g, \\quad\\text{in}\\; \\Omega.\n",
        "    \\end{aligned}\n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nMBZy9lg6K8W"
      },
      "source": [
        "We present a **four-field formulation** that facilitates the derivation of locking-free discretizations. It is obtained by introducing the additional variable \n",
        "\n",
        "$$\n",
        "\\varphi = \\lambda \\boldsymbol\\nabla\\cdot\\boldsymbol{u} - \\alpha p -\\beta T.\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZeCp00tQGvUw"
      },
      "source": [
        "### Semi-discrete weak formulation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4ho2Ci6j7vWm"
      },
      "source": [
        "By testing with sufficiently regular functions, integrating by parts, and assuming for simplicity homogeneous Dirichlet boundary conditions for all primary variables, we get the following weak form of the problem:\n",
        "\n",
        "$$\n",
        "    \\begin{aligned}\n",
        "(2\\mu\\boldsymbol\\nabla_s\\boldsymbol{u}, \\boldsymbol\\nabla_s\\boldsymbol{v})_\\Omega  + (\\varphi,\\boldsymbol\\nabla\\cdot\\boldsymbol{v})_\\Omega &= (\\boldsymbol{f}, \\boldsymbol{v})_\\Omega, \\\\\n",
        "(\\lambda^{-1}(\\varphi+\\alpha p+\\beta T),\\psi)_\\Omega - (\\psi,\\boldsymbol\\nabla\\cdot\\boldsymbol{u})_\\Omega &= 0, \\\\\n",
        "((a_0+\\beta^2 \\lambda^{-1}) \\partial_t T, S)_\\Omega \n",
        "+ (\\beta\\lambda^{-1}\\partial_t \\varphi, S)_\\Omega \n",
        "+((\\alpha\\beta\\lambda^{-1} - b_0) \\partial_t p, S)_\\Omega +(\\Theta\\boldsymbol\\nabla T, \\boldsymbol\\nabla S)_\\Omega &= (h, S)_\\Omega,  \\\\\n",
        "((c_0+\\alpha^2 \\lambda^{-1}) \\partial_t p, q)_\\Omega \n",
        "+ (\\alpha\\lambda^{-1}\\partial_t \\varphi, q)_\\Omega \n",
        "+((\\alpha\\beta\\lambda^{-1} - b_0) \\partial_t T, q)_\\Omega +(\\kappa\\boldsymbol\\nabla p, \\boldsymbol\\nabla q)_\\Omega &= (g, S)_\\Omega.\n",
        "    \\end{aligned}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F3lp1-ucGAF-"
      },
      "source": [
        "Deriving the second equation in time, summing the resulting four equations, and rearranging, yields the *semi-discrete total weak formulation*, which is used as a strarting point for the derivation of the dG discretization below. The **semi-discrete weak problem** reads: Find $(\\boldsymbol{u}, p, T, \\varphi)$ in $\\boldsymbol{H}^1_0(\\Omega)\\times{H}^1_0(\\Omega)\\times{H}^1_0(\\Omega)\\times L^2(\\Omega)$, such that, for all $(\\boldsymbol{v}, q, S, \\psi)$ in $\\boldsymbol{H}^1_0(\\Omega)\\times{H}^1_0(\\Omega)\\times{H}^1_0(\\Omega)\\times L^2(\\Omega)$, \n",
        "\n",
        "$$\n",
        "(2\\mu\\boldsymbol\\nabla_s\\boldsymbol{u}, \\boldsymbol\\nabla_s\\boldsymbol{v})_\\Omega  \n",
        "+ (\\varphi,\\boldsymbol\\nabla\\cdot\\boldsymbol{v})_\\Omega \n",
        "- (\\psi,\\boldsymbol\\nabla\\cdot\\boldsymbol{u})_\\Omega\n",
        "+(\\Theta\\boldsymbol\\nabla T, \\boldsymbol\\nabla S)_\\Omega \n",
        "+(\\kappa\\boldsymbol\\nabla p, \\boldsymbol\\nabla q)_\\Omega\n",
        "+(\\lambda^{-1}\\partial_t (\\varphi+\\alpha p+\\beta T),\\psi + \\alpha q + \\beta S)_\\Omega \n",
        "+ b_0 (\\partial_t(p-T), q-S)_\\Omega \n",
        "+ ((a_0-b_0) \\partial_t T, S)_\\Omega \n",
        "+ ((c_0-b_0) \\partial_t p, q)_\\Omega = (\\boldsymbol{f}, \\boldsymbol{v})_\\Omega + (h, S)_\\Omega + (g, q)_\\Omega.\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zzNdaNWQKAHU"
      },
      "source": [
        "The **well-posedness** of the previous problem follows by taking $\\boldsymbol{v} = \\partial_t \\boldsymbol{u}$, $S = T$, $p = q$, and $\\psi = \\varphi$ and observing that all the terms appearing on the left-hand side of the resulting equation are positive. The ellpitic terms provides the control of the $H^1_0$-norms of the primary varibles and the classical inf-sup argument gives the bound of the $L^2$-norm of $\\varphi$. The a-priori bound is then obtained via standard arguments. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hiJsD_DWLkt3"
      },
      "source": [
        "In the following FEniCS implementation the **fully-discrete formulation** is obtained by considering a backward Euler time advancing scheme. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yLEWqE0u3jKb"
      },
      "source": [
        "## Convergence test "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7bVBRFliIY8d"
      },
      "source": [
        "On the unit square domain $\\Omega = (0,1) \\times (0,1)$ and time interval $I = (0, 1)$ \n",
        "we consider the initial and boundary value problem (corresponding to the thermoporoelasticity system) assuming as analytical solution:\n",
        "$$\n",
        "    \\begin{aligned}\n",
        "      u_1 &= (e^{t} - 1) (\\sin(2\\pi y) (\\cos(2 \\pi x) - 1) + \\frac1{\\mu +\\lambda} \\sin(\\pi x) \\sin(\\pi y)), \\\\\n",
        "      u_2 &= (e^{t} - 1) (\\sin(2\\pi x) (1 - \\cos(2 \\pi y)) + \\frac1{\\mu +\\lambda} \\sin(\\pi x) \\sin(\\pi y)), \\\\\n",
        "      p &= (e^{t} - 1) \\sin(\\pi x) \\sin(\\pi y), \\\\\n",
        "      T &= (e^{t} - 1) (\\cos(2 \\pi x) - 1) (\\cos(2 \\pi y) - 1).\n",
        "    \\end{aligned}\n",
        "$$\n",
        "\n",
        "Hence, we have $\\boldsymbol{u}_{|\\partial\\Omega} = \\boldsymbol{0}$, $p_{|\\partial\\Omega} = 0$, $T_{|\\partial\\Omega} = 0$, $\\boldsymbol{u}(0) = \\boldsymbol{u}_{0} = \\boldsymbol{0}$, $p(0) = p_{0} = 0$, and $T(0) = 0$. The right-hand side terms inferred from the exact solution are\n",
        "$$\n",
        "    \\begin{aligned}\n",
        "      f_1 &= \\pi(e^t - 1)\\left(\\alpha\\cos(\\pi x)\\sin(\\pi y)-2\\beta\\sin(2\\pi x)(cos(2\\pi y)-1)-\\pi(\\cos(\\pi x+\\pi y)+4\\mu\\sin(2\\pi y)(1-2\\cos(2\\pi x))-\\frac{2\\mu\\sin(\\pi x)\\sin(\\pi y)}{\\mu +\\lambda}\\right), \\\\\n",
        "      f_2 &= \\pi(e^t - 1)\\left(\\alpha\\sin(\\pi x)\\cos(\\pi y)-2\\beta\\sin(2\\pi y)(cos(2\\pi x)-1)-\\pi(\\cos(\\pi x+\\pi y)+4\\mu\\sin(2\\pi x)(2\\cos(2\\pi y)-1)-\\frac{2\\mu\\sin(\\pi x)\\sin(\\pi y)}{\\mu +\\lambda}\\right), \\\\\n",
        "      g &= (2\\kappa\\pi^2 (e^{t} - 1) + c_0 e^t) \\sin(\\pi x) \\sin(\\pi y) - b_0 e^t (cos(2\\pi x)-1)(cos(2\\pi y)-1) + \\frac{\\alpha\\pi e^t}{\\lambda + \\mu} \\sin(\\pi x + \\pi y), \\\\ \n",
        "      h &= (4\\Theta\\pi^2 (e^{t} - 1) + a_0 e^t) (cos(2\\pi x)-1)(cos(2\\pi y)-1) + 4\\Theta\\pi^2 (e^{t} - 1)(cos(2\\pi x)cos(2\\pi y) -1) - b_0 e^t \\sin(\\pi x) \\sin(\\pi y) + \\frac{\\beta\\pi e^t \\sin(\\pi x + \\pi y)}{\\lambda + \\mu} .\n",
        "    \\end{aligned}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1uL_AH6Je4Le"
      },
      "source": [
        "## Import FEniCS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZNGbzoV3eFJT"
      },
      "source": [
        "%%capture\n",
        "try:\n",
        "    import dolfin\n",
        "except ImportError:\n",
        "    !wget \"https://fem-on-colab.github.io/releases/fenics-install.sh\" -O \"/tmp/fenics-install.sh\" && bash \"/tmp/fenics-install.sh\"\n",
        "    import dolfin"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v57eOLIIe2fa"
      },
      "source": [
        "from fenics import *\n",
        "from mshr import *\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7yweE9IzJ2Dx"
      },
      "source": [
        "## Declare problem data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bOfg-_vPe_NQ"
      },
      "source": [
        "# problem data\n",
        "T = 0.6               # final simulation time\n",
        "mu = Constant(1.0)    # mu fixed as reference parameter (keep it = 1)\n",
        "lam = Constant(5.0)   # lam can be arbitrarly large (nearly incompressible case)\n",
        "a_0 = Constant(0.02)  # a_0 can be equal to 0\n",
        "b_0 = Constant(0.01)  # b_0 < a_0 and b_0 < c_0 (physical constraints)\n",
        "c_0 = Constant(0.03)  # c_0 can be equal to 0\n",
        "kappa = Constant(0.2) # strictly positive\n",
        "theta = Constant(0.05)# strictly positive\n",
        "alpha = Constant(1.0) # strictly positive and smaller or equal to 1\n",
        "beta = Constant(0.8)  # strictly positive and smaller or equal to 1\n",
        "\n",
        "# volumetric forcing term\n",
        "f1 = Expression((\n",
        "    'pi*(exp(time)-1)*(_alpha*cos(pi*x[0])*sin(pi*x[1]) -2*_beta*sin(2*pi*x[0])*(cos(2*pi*x[1])-1) -pi*(cos(pi*x[0]+pi*x[1])+4*sin(2*pi*x[1])*(1-2*cos(2*pi*x[0]))))', \n",
        "    'pi*(exp(time)-1)*(_alpha*sin(pi*x[0])*cos(pi*x[1]) -2*_beta*sin(2*pi*x[1])*(cos(2*pi*x[0])-1) -pi*(cos(pi*x[0]+pi*x[1])+4*sin(2*pi*x[0])*(2*cos(2*pi*x[1])-1)))'\n",
        "              ), degree=3, time=0.0, _alpha=alpha, _beta=beta)\n",
        "f2 = Expression((\n",
        "    '(2*_mu/(_mu+_lam))*pi*pi*(exp(time)-1)*(sin(pi*x[0])*sin(pi*x[1]))', \n",
        "    '(2*_mu/(_mu+_lam))*pi*pi*(exp(time)-1)*(sin(pi*x[0])*sin(pi*x[1]))'\n",
        "              ), degree=3, time=0.0, _mu=1.0, _lam=lam)\n",
        "\n",
        "# fluid source term\n",
        "g1 = Expression('(_kappa*2*pi*pi*(exp(time)-1)+_c_0*exp(time))*sin(pi*x[0])*sin(pi*x[1])', degree=3, time=0.0, _kappa=kappa, _c_0=c_0) \n",
        "g2 = Expression('(_alpha*pi/(_mu+_lam))*exp(time)*sin(pi*x[0]+pi*x[1])-_b_0*exp(time)*(cos(2*pi*x[0])-1)*(cos(2*pi*x[1])-1)', degree=3, time=0.0, _mu=1.0, _lam=lam, _b_0=b_0, _alpha=alpha)\n",
        "\n",
        "# thermal source term\n",
        "h1 = Expression('(_theta*4*pi*pi*(exp(time)-1)+_a_0*exp(time))*(cos(2*pi*x[0])-1)*(cos(2*pi*x[1])-1)+_theta*4*pi*pi*(exp(time)-1)*(cos(2*pi*x[0])*cos(2*pi*x[1])-1)', degree=3, time=0.0, _theta=theta, _a_0=a_0) \n",
        "h2 = Expression('(_beta*pi/(_mu+_lam))*exp(time)*sin(pi*x[0]+pi*x[1])-_b_0*exp(time)*sin(pi*x[0])*sin(pi*x[1])', degree=3, time=0.0, _mu=1.0, _lam=lam, _b_0=b_0, _beta=beta)\n",
        "\n",
        "# analytical solutions (primary variables)\n",
        "u_ex = Expression((\n",
        "      '(exp(time)-1)*(sin(2*pi*x[1])*(cos(2*pi*x[0])-1) + (1.0/(_mu+_lam))*sin(pi*x[0])*sin(pi*x[1]))', \n",
        "      '(exp(time)-1)*(sin(2*pi*x[0])*(1-cos(2*pi*x[1])) + (1.0/(_mu+_lam))*sin(pi*x[0])*sin(pi*x[1]))'\n",
        "              ), degree=4, time=0.0, _mu=1.0, _lam=lam)\n",
        "p_ex = Expression('(exp(time)-1)*sin(pi*x[0])*sin(pi*x[1])', degree=4, time=0.0)\n",
        "T_ex = Expression('(exp(time)-1)*(cos(2*pi*x[0])-1)*(cos(2*pi*x[1])-1)', degree=4, time=0.0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ygkLsxQ_K5tM"
      },
      "source": [
        "## Implementation of equal order dG scheme"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ro00GiW0Jvuk"
      },
      "source": [
        "def dg_ThePorEl4f(n, deg, dt, T, lam, a_0, b_0, c_0, kappa, theta, alpha, beta, u_ex, p_ex, T_ex, f1, f2, g1, g2, h1, h2):\n",
        "    # 0. method specific pre-computations\n",
        "    gamma = 9.1*deg**2\n",
        "    delta = 3.1/deg\n",
        "\n",
        "    # 1. mesh generation\n",
        "    #mesh = UnitSquareMesh(n, n, 'crossed')\n",
        "    square = Rectangle(Point(0.0, 0.0), Point(1.0, 1.0))\n",
        "    mesh = generate_mesh(square, n)\n",
        "\n",
        "    # 2. definition of the lowest-order Taylor-Hood finite element pair\n",
        "    U = VectorElement('DG', mesh.ufl_cell(), deg)\n",
        "    Q = FiniteElement('DG', mesh.ufl_cell(), deg)\n",
        "    P = FiniteElement('DG', mesh.ufl_cell(), deg)\n",
        "    X = FunctionSpace(mesh, MixedElement([U, Q, P, P]))\n",
        "\n",
        "    # 3a. assembling: def functions and operators \n",
        "    u, phi, p, tt = TrialFunctions(X)\n",
        "    v, psi, q, rr = TestFunctions(X)\n",
        "    x_old = Function(X)\n",
        "    u_old, phi_old, p_old, tt_old = split(x_old)\n",
        "    \n",
        "    n = FacetNormal(mesh)\n",
        "    h = CellDiameter(mesh)\n",
        "    h_avg = (h('+') + h('-'))/2\n",
        "\n",
        "    # 3b. assembling : def forms\n",
        "    a1 = (2.0*inner(sym(grad(u)), sym(grad(v))) + phi*div(v) - div(u)*psi)*dx  \\\n",
        "       - 2.0*inner(dot(avg(sym(grad(u))), n('+')), jump(v))*dS \\\n",
        "       - 2.0*inner(jump(u), dot(avg(sym(grad(v))), n('+')))*dS \\\n",
        "       - 2.0*inner(dot(sym(grad(u)), n), v)*ds \\\n",
        "       - 2.0*inner(u, dot(sym(grad(v)), n))*ds \\\n",
        "       + 2.0*gamma/h_avg*inner(jump(u), jump(v))*dS \\\n",
        "       + 2.0*gamma/h*inner(u, v)*ds \\\n",
        "       + inner(jump(u, n), avg(psi))*dS - inner(jump(v, n), avg(phi))*dS \\\n",
        "       + inner(u, n)*psi*ds - inner(v, n)*phi*ds \\\n",
        "       + delta*h_avg*jump(phi)*jump(psi)*dS \n",
        "\n",
        "    a2 = (1.0/lam)*(phi+alpha*p+beta*tt)*(psi+alpha*q+beta*rr)*dx \\\n",
        "       + (b_0*(p-tt)*(q-rr) + (c_0-b_0)*p*q + (a_0-b_0)*tt*rr)*dx\n",
        "\n",
        "    a3 = dt*kappa*dot(grad(p), grad(q))*dx \\\n",
        "       - dt*kappa*dot(avg(grad(q)), jump(p, n))*dS \\\n",
        "       - dt*kappa*dot(jump(q, n), avg(grad(p)))*dS \\\n",
        "       - dt*kappa*(dot(grad(q), p*n) + dot(q*n, grad(p)))*ds \\\n",
        "       + dt*kappa*gamma/h_avg*dot(jump(p, n), jump(q, n))*dS \\\n",
        "       + dt*kappa*gamma/h*p*q*ds\n",
        "\n",
        "    a4 = dt*theta*dot(grad(tt), grad(rr))*dx \\\n",
        "       - dt*theta*dot(avg(grad(rr)), jump(tt, n))*dS \\\n",
        "       - dt*theta*dot(jump(rr, n), avg(grad(tt)))*dS \\\n",
        "       - dt*theta*(dot(grad(rr), tt*n) + dot(rr*n, grad(tt)))*ds \\\n",
        "       + dt*theta*gamma/h_avg*dot(jump(tt, n), jump(rr, n))*dS \\\n",
        "       + dt*theta*gamma/h*tt*rr*ds\n",
        "    \n",
        "    a = a1 + a2 + a3 + a4   \n",
        "    \n",
        "    L = (dot(f1+f2, v) + dt*(g1+g2)*q + dt*(h1+h2)*rr)*dx \\\n",
        "      + (p_old*(c_0*q-b_0*rr) + tt_old*(a_0*rr-b_0*q))*dx \\\n",
        "      + (1/lam)*(alpha*p_old+beta*tt_old+phi_old)*(alpha*q+beta*rr)*dx\n",
        "\n",
        "    # 4. solve and advance in time \n",
        "    A = assemble(a)\n",
        "    Ainv = LUSolver(A)\n",
        "\n",
        "    l2err_u = 0.0\n",
        "    h1err_u = 0.0\n",
        "    l2err_p = 0.0\n",
        "    h1err_p = 0.0\n",
        "    l2err_t = 0.0\n",
        "    h1err_t = 0.0\n",
        "\n",
        "    for t in np.arange(dt, T+0.1*dt, dt):\n",
        "        f1.time = t\n",
        "        f2.time = t\n",
        "        g1.time = t\n",
        "        g2.time = t\n",
        "        h1.time = t\n",
        "        h2.time = t\n",
        "        b = assemble(L)\n",
        "        \n",
        "        print('solving time {}'.format(t))\n",
        "        Ainv.solve(x_old.vector(), b)\n",
        "        u_old, phi_old, p_old, tt_old = x_old.split()\n",
        "\n",
        "        u_ex.time = t\n",
        "        p_ex.time = t\n",
        "        T_ex.time = t\n",
        "        l2err_u = max(l2err_u, errornorm(u_ex, u_old, 'L2'))\n",
        "        h1err_u += dt * (errornorm(u_ex, u_old, 'H10')**2)\n",
        "        l2err_p = max(l2err_p, errornorm(p_ex, p_old, 'L2'))\n",
        "        h1err_p += dt * (errornorm(p_ex, p_old, 'H10')**2)\n",
        "        l2err_t = max(l2err_t, errornorm(T_ex, tt_old, 'L2'))\n",
        "        h1err_t += dt * (errornorm(T_ex, tt_old, 'H10')**2)\n",
        "    \n",
        "    h1err_u = sqrt(h1err_u)\n",
        "    h1err_p = sqrt(h1err_p)\n",
        "    h1err_t = sqrt(h1err_t)\n",
        "    return l2err_u, h1err_u, l2err_p, h1err_p, l2err_t, h1err_t"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qa4O5niUPzEE",
        "outputId": "f6b733b1-1c99-4b01-f46b-f11bc9e33a7a"
      },
      "source": [
        "M_err=np.zeros((6,4))\n",
        "deg = 1\n",
        "\n",
        "for i in range(4):\n",
        "    n = 5*(2**i)\n",
        "    dt = 0.3/(4**i)\n",
        "    l2err_u, h1err_u, l2err_p, h1err_p, l2err_t, h1err_t = dg_ThePorEl4f(n, deg, dt, T, lam, a_0, b_0, c_0, kappa, theta, alpha, beta, u_ex, p_ex, T_ex, f1, f2, g1, g2, h1, h2)\n",
        "\n",
        "    M_err[0,i] = l2err_u \n",
        "    M_err[1,i] = h1err_u\n",
        "    M_err[2,i] = l2err_p \n",
        "    M_err[3,i] = h1err_p\n",
        "    M_err[4,i] = l2err_t \n",
        "    M_err[5,i] = h1err_t\n",
        "\n",
        "    print('n={} dt={} l2err_u={:.2e} h1err_u={:.2e} l2err_p={:.2e} h1err_p={:.2e} l2err_t={:.2e} h1err_t={:.2e}'.format(n, dt, l2err_u, h1err_u, l2err_p, h1err_p, l2err_t, h1err_t))\n",
        "    print()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "solving time 0.3\n",
            "solving time 0.6\n",
            "n=5 dt=0.3 l2err_u=1.11e-01 h1err_u=1.40e+00 l2err_p=1.57e-02 h1err_p=2.07e-01 l2err_t=6.85e-02 h1err_t=1.14e+00\n",
            "\n",
            "solving time 0.075\n",
            "solving time 0.15\n",
            "solving time 0.22499999999999998\n",
            "solving time 0.3\n",
            "solving time 0.375\n",
            "solving time 0.45\n",
            "solving time 0.5249999999999999\n",
            "solving time 0.6\n",
            "n=10 dt=0.075 l2err_u=3.08e-02 h1err_u=5.53e-01 l2err_p=3.86e-03 h1err_p=7.82e-02 l2err_t=1.82e-02 h1err_t=4.40e-01\n",
            "\n",
            "solving time 0.01875\n",
            "solving time 0.0375\n",
            "solving time 0.056249999999999994\n",
            "solving time 0.075\n",
            "solving time 0.09375\n",
            "solving time 0.1125\n",
            "solving time 0.13124999999999998\n",
            "solving time 0.15\n",
            "solving time 0.16874999999999998\n",
            "solving time 0.18749999999999997\n",
            "solving time 0.20625\n",
            "solving time 0.22499999999999998\n",
            "solving time 0.24374999999999997\n",
            "solving time 0.2625\n",
            "solving time 0.28125\n",
            "solving time 0.3\n",
            "solving time 0.31875\n",
            "solving time 0.33749999999999997\n",
            "solving time 0.35624999999999996\n",
            "solving time 0.375\n",
            "solving time 0.39375\n",
            "solving time 0.4125\n",
            "solving time 0.43124999999999997\n",
            "solving time 0.44999999999999996\n",
            "solving time 0.46874999999999994\n",
            "solving time 0.4875\n",
            "solving time 0.50625\n",
            "solving time 0.525\n",
            "solving time 0.5437500000000001\n",
            "solving time 0.5625\n",
            "solving time 0.58125\n",
            "solving time 0.6\n",
            "n=20 dt=0.01875 l2err_u=8.43e-03 h1err_u=2.66e-01 l2err_p=1.02e-03 h1err_p=3.72e-02 l2err_t=5.07e-03 h1err_t=2.09e-01\n",
            "\n",
            "solving time 0.0046875\n",
            "solving time 0.009375\n",
            "solving time 0.014062499999999999\n",
            "solving time 0.01875\n",
            "solving time 0.0234375\n",
            "solving time 0.028125\n",
            "solving time 0.032812499999999994\n",
            "solving time 0.0375\n",
            "solving time 0.042187499999999996\n",
            "solving time 0.04687499999999999\n",
            "solving time 0.0515625\n",
            "solving time 0.056249999999999994\n",
            "solving time 0.06093749999999999\n",
            "solving time 0.065625\n",
            "solving time 0.0703125\n",
            "solving time 0.075\n",
            "solving time 0.0796875\n",
            "solving time 0.08437499999999999\n",
            "solving time 0.08906249999999999\n",
            "solving time 0.09375\n",
            "solving time 0.0984375\n",
            "solving time 0.103125\n",
            "solving time 0.10781249999999999\n",
            "solving time 0.11249999999999999\n",
            "solving time 0.11718749999999999\n",
            "solving time 0.121875\n",
            "solving time 0.1265625\n",
            "solving time 0.13125\n",
            "solving time 0.13593750000000002\n",
            "solving time 0.140625\n",
            "solving time 0.1453125\n",
            "solving time 0.15\n",
            "solving time 0.1546875\n",
            "solving time 0.15937500000000002\n",
            "solving time 0.1640625\n",
            "solving time 0.16875\n",
            "solving time 0.1734375\n",
            "solving time 0.178125\n",
            "solving time 0.18281250000000002\n",
            "solving time 0.1875\n",
            "solving time 0.1921875\n",
            "solving time 0.196875\n",
            "solving time 0.2015625\n",
            "solving time 0.20625000000000002\n",
            "solving time 0.2109375\n",
            "solving time 0.215625\n",
            "solving time 0.2203125\n",
            "solving time 0.225\n",
            "solving time 0.2296875\n",
            "solving time 0.234375\n",
            "solving time 0.2390625\n",
            "solving time 0.24375\n",
            "solving time 0.2484375\n",
            "solving time 0.253125\n",
            "solving time 0.2578125\n",
            "solving time 0.2625\n",
            "solving time 0.2671875\n",
            "solving time 0.271875\n",
            "solving time 0.2765625\n",
            "solving time 0.28125\n",
            "solving time 0.2859375\n",
            "solving time 0.290625\n",
            "solving time 0.2953125\n",
            "solving time 0.3\n",
            "solving time 0.3046875\n",
            "solving time 0.309375\n",
            "solving time 0.3140625\n",
            "solving time 0.31875\n",
            "solving time 0.3234375\n",
            "solving time 0.328125\n",
            "solving time 0.3328125\n",
            "solving time 0.3375\n",
            "solving time 0.3421875\n",
            "solving time 0.346875\n",
            "solving time 0.3515625\n",
            "solving time 0.35625\n",
            "solving time 0.3609375\n",
            "solving time 0.365625\n",
            "solving time 0.3703125\n",
            "solving time 0.375\n",
            "solving time 0.3796875\n",
            "solving time 0.384375\n",
            "solving time 0.3890625\n",
            "solving time 0.39375\n",
            "solving time 0.3984375\n",
            "solving time 0.403125\n",
            "solving time 0.4078125\n",
            "solving time 0.4125\n",
            "solving time 0.4171875\n",
            "solving time 0.421875\n",
            "solving time 0.4265625\n",
            "solving time 0.43125\n",
            "solving time 0.4359375\n",
            "solving time 0.440625\n",
            "solving time 0.4453125\n",
            "solving time 0.45\n",
            "solving time 0.45468749999999997\n",
            "solving time 0.459375\n",
            "solving time 0.4640625\n",
            "solving time 0.46875\n",
            "solving time 0.4734375\n",
            "solving time 0.47812499999999997\n",
            "solving time 0.4828125\n",
            "solving time 0.4875\n",
            "solving time 0.4921875\n",
            "solving time 0.496875\n",
            "solving time 0.5015624999999999\n",
            "solving time 0.50625\n",
            "solving time 0.5109374999999999\n",
            "solving time 0.5156249999999999\n",
            "solving time 0.5203125\n",
            "solving time 0.5249999999999999\n",
            "solving time 0.5296875\n",
            "solving time 0.5343749999999999\n",
            "solving time 0.5390624999999999\n",
            "solving time 0.54375\n",
            "solving time 0.5484374999999999\n",
            "solving time 0.553125\n",
            "solving time 0.5578124999999999\n",
            "solving time 0.5624999999999999\n",
            "solving time 0.5671875\n",
            "solving time 0.5718749999999999\n",
            "solving time 0.5765625\n",
            "solving time 0.5812499999999999\n",
            "solving time 0.5859374999999999\n",
            "solving time 0.590625\n",
            "solving time 0.5953124999999999\n",
            "solving time 0.6\n",
            "n=40 dt=0.0046875 l2err_u=2.13e-03 h1err_u=1.29e-01 l2err_p=2.49e-04 h1err_p=1.79e-02 l2err_t=1.29e-03 h1err_t=1.02e-01\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "krO8kC7QF30e"
      },
      "source": [
        "### Plot convergence results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "N8JI2fXhP-D3",
        "outputId": "a1a26ded-0544-4a39-bfd2-949ff724d421"
      },
      "source": [
        "# definition of the meshsize \n",
        "h = np.array([0.2/(2**i) for i in range(4)])\n",
        "\n",
        "# we use the subplots axis layout managers in matplotlib\n",
        "fig, axes = plt.subplots(figsize=(8,6))\n",
        "\n",
        "axes.loglog(h, h, 'silver',label=\"order 1\")\n",
        "axes.loglog(h, h**2, 'coral',label=\"order 2\")\n",
        "#axes.loglog(h, h**3, 'm',label=\"order 3\")\n",
        "axes.loglog(h, M_err[0,:], 'r--o',label=\"$L^2$ err u\")\n",
        "axes.loglog(h, M_err[1,:], 'g--*',label=\"$H^1$ err u\")\n",
        "axes.loglog(h, M_err[2,:], 'k--o',label=\"$L^2$ err p\")\n",
        "axes.loglog(h, M_err[3,:], 'b--*',label=\"$H^1$ err p\")\n",
        "axes.loglog(h, M_err[4,:], 'm--o',label=\"$L^2$ err t\")\n",
        "axes.loglog(h, M_err[5,:], 'c--*',label=\"$H^1$ err t\")\n",
        "\n",
        "axes.set_title(\"convergence for equal-order dG scheme\");\n",
        "axes.set_xlabel(\"h\")\n",
        "axes.set_ylabel(\"errors\")\n",
        "axes.legend(loc=4)\n",
        "\n",
        "fig.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fg6PR3SfQo37"
      },
      "source": [],
      "execution_count": null,
      "outputs": []
    }
  ]
}