L2_projection_error_and_optimality.ipynb

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
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   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'ax' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-63-c4f45474c6ab>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     39\u001b[0m \u001b[0me\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mu\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mu0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     40\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 41\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcla\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     42\u001b[0m \u001b[0mfig2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgcf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m \u001b[0mfig2\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mset_size_inches\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m16\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m6.5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     43\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m \u001b[0mpp2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmplot_function\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mu0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'ax' is not defined"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%run /home/fenics/fenics-matplotlib.py\n",
    "from dolfin import *; from mshr import *; from IPython.display import display, clear_output; import time\n",
    "import logging; logging.getLogger('FFC').setLevel(logging.WARNING)\n",
    "import numpy as np\n",
    "\n",
    "#Define domain and mesh\n",
    "a,b = 0,1\n",
    "mresolution = 100\n",
    "mesh = IntervalMesh(mresolution,a,b)\n",
    "\n",
    "#Define finite element function space\n",
    "p_order =1;\n",
    "V = FunctionSpace(mesh,\"CG\",p_order)\n",
    "\n",
    "#Express the \"exact\" reference function\n",
    "u = Expression(\"1 + sin(10*x[0])\",degree=5,domain=mesh)\n",
    "\n",
    "#Interpolate u onto V\n",
    "Iu = interpolate(u,V)\n",
    "\n",
    "#Project u onto V\n",
    "Pu = project(u,V)\n",
    "u0 = Pu\n",
    "#print u - u0\n",
    "\n",
    "#Define a function to explicitly evaluate the expression\n",
    "#w = Function(V)\n",
    "#wa = w.vector().array()\n",
    "#Extract vertices of the mesh\n",
    "#x = V.dofmap().tabulate_all_coordinates(mesh)\n",
    "#indices = np.argsort(x)\n",
    "#for j in indices:\n",
    " #   wa[j] = u(x[j])\n",
    "#    \n",
    "#Pua = Pu.vector().array()\n",
    "\n",
    "\n",
    "e = u - u0\n",
    "import matplotlib.pyplot as plt\n",
    "ax.cla(); \n",
    "fig2 = plt.gcf(); fig2.set_size_inches(16,6.5)\n",
    "plt.subplot(1,2,2); pp2 = mplot_function(u0);\n",
    "plt.colorbar(pp2)\n",
    "print e\n",
    "e1 = sqrt(assemble((u -u0)*(u - u0)*dx))\n",
    "e2 = sqrt(assemble(u*u*dx))\n",
    "re = (e1/e2);\n",
    "#print re\n",
    "print e1\n",
    "#print e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'ax' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-68-769ee5b553d2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcla\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'ax' is not defined"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "ax.cla()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'ax' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-66-913d060aeb24>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mlogging\u001b[0m\u001b[1;33m;\u001b[0m \u001b[0mlogging\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mgetLogger\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'FFC'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msetLevel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogging\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mWARNING\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcla\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'ax' is not defined"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%run /home/fenics/fenics-matplotlib.py\n",
    "from dolfin import *; from mshr import *; from IPython.display import display, clear_output; import time\n",
    "import logging; logging.getLogger('FFC').setLevel(logging.WARNING)\n",
    "import matplotlib.pyplot as plt\n",
    "ax.cla();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'ax' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-67-769ee5b553d2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpyplot\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcla\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'ax' is not defined"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "ax.cla()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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