Heat-Equation/main.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#1 Loading functions  and modules\n",
    "from fenics import *\n",
    "import matplotlib.pyplot as plt\n",
    "T = 2.0\n",
    "num_steps = 20\n",
    "dt = T/num_steps\n",
    "rho = 7500\n",
    "Cp = 500\n",
    "k = 50\n",
    "alpha = k/(rho*Cp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAACgCAYAAAAM9xtHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzsvXl0G9eZJX6LWEiCG0CCxMJ9AcEFZIE7JWs1rcWyLMmSZcuSvMiRJVmy40WxezoTZ+vjOHEnnenTm9uJx2c880t34nYcJUrS09NuO9pFiiLADaRIivtOgAAXECBB1u8P6j1XAQWJluUlCb5zdI4AfgCqLh7qvfru9+5lOI5DKEIRilCEIhRhX/QBhCIUoQhFKL4cEZoQQhGKUIQiFABCE0IoQhGKUITiRoQmhFCEIhShCAWA0IQQilCEIhShuBGhCSEUoQhFKEIBIDQhhCIUoQhFKG5EaEIIRShCEYpQAAhNCKEIRShCEYobIf2iD+CThFqt5jIyMr7owwhFKEIRij+aqK+vn+A4LnEluX9UE0JGRgauXLnyRR9GKEIRilD80QTDML0rzV1RyYhhmK0Mw7QzDNPJMMx/E/l7OMMwP7/x98sMw2Tw/vaXN55vZxhmy43nIhiGqWUYxsowTAvDMN9Z6QGHIhShCEUoPpu45YTAMIwEwD8AuBdAAYBHGIYp8Ev7CoBJjuNyAPwYwA9uvLYAwD4AhQC2AvjHG+/nBXA3x3EsADOArQzDVN+ZUwpFKEIRilDcTqzkDqESQCfHcdc5jpsH8K8Advrl7ATwv278/98A1DAMw9x4/l85jvNyHNcNoBNAJbccMzfyZTf+fWayqytVdP2y532Rn/1lz/siP/vLnvdFfvYXmffHcIxftlgJh5AMoJ/3eABAVbAcjuN8DMO4ACTceP6S32uTAXrnUQ8gB8A/cBx3+XZO4FbBcRy++93v0sc6nQ7Lc1VgDA0NfeI8jUYDiURyyzy1Wg25XH7LPKVSCYVCccu8qKgoxMXFieaNjY3B5/MBAGQyGRITxfkkjuMwPDxMH6/0nLVaLcLCxNcSX3ZsJicnMTc3B+Dm2Pi/553GJikpCVKp+M+Pn5eQkIDw8PBb5sXFxSEqKuqWeQqFAkqlUjRvZmYGU1NTAACpVIqkpCTRPP/3/FPBJjIyEiqVSjRvbm4Ok5OTAACJRAKNRiOa5/+edxKbb33rW0E/807FF0Yqcxy3CMDMMIwSwPsMw5g4jmv2z2MY5giAIwCQlpb2iT9nYWFB8JhcALVaLWJiYvjHI5qXkJCA+Pj4oO8/OjoKAIiJiYFWqw2aNzExAQCQy+VIS0sLOkicTiecTicAICsrK+gFdXZ2FrOzswCWyXaZTCaat7CwQAdUSkoKIiMjBX/jx0qxGRkZAQDEx8cjISFB9HOBj7GJjo6GVqsNes4EG5lMhvT09M8UG/J64ObYkAmVBMFGo9EgNjY2yBl/jI1KpYJarQ6aNzY2BmB58rrZRcNutwNYvkBnZGQEzXO5XHC5XABujo3b7Ybb7QYApKenCyZighmwfP4Em+TkZMFEvLi4KHhPgk1SUlLQiRj45NgoFAro9fpbYiORSJCZmfmpsZmbm6OLBX9svF4v/f/i4uJnho1SqbzpIuWzjpVMCIMAUnmPU248J5YzwDCMFEAcAPtKXstxnJNhmA+xzDEETAgcx70J4E0AKC8v/8T3WHK5HDKZDEVFRdDr9bBarejv78fo6ChiYmJgNpuRm5sLqVSKN954A9HR0TCbzbBarejq6oLdbkdUVBTMZjMKCgoQHh6Od999FyMjI9i6dSssFgva29sxPT0NhUIBs9mMoqIiREVF4YMPPsD58+fxxBNPwGKxoKWlBfPz87Db7WBZFizLQqlUwmKx4NSpU9i3bx96enrQ1NSE2dlZjI6Oori4GGazGUlJSejr68Pbb7+N7du3Y3p6GlarFU6nE8PDwygsLITZbEZKSgrcbjd++MMfYt26dYiIiIDFYsHY2BiGh4eRl5cHs9mMrKwshIWF4fvf/z7y8/ORmpoKq9WKvr4+jI6OUhyMRiOkUil+8pOfIDw8HGVlZbBYLOjq6oLD4aDYFBYWIjw8HO+99x4GBwexbds2WCwWtLW10ZUnwSY6Ohoffvghzpw5gyeffJJi4/V6MTExQbFRqVRobGzE+++/j4ceegj9/f1obGzE7OwsRkZGKDYajQaDg4P46U9/im3btsHtdsNiscDpdGJoaIhik5qaCo/Hg9dffx1r1qxBVFQULBYLRkdHMTw8DKPRCLPZjOzsbISFheH111+HwWBARkYGLBYL+vr6MDY2JsBGJpPhrbfegkQiQWVlJSwWCzo7OzE5OSnAJiIiAr/61a/Q3d2NHTt2UGxmZ2fhcrlgNptRXFyM6OhonDlzBh9++CEOHTqExsZGNDc3w+v1Ynx8nGITHx+P5uZmvPfee9i7dy8GBwfR2NiImZkZjIyMoKioCGazGVqtFsPDw3jzzTexdetWeL1eWCwWTE5OYnh4GAUFBTCbzUhLS8PCwgJee+01rF69GrGxsbBYLBgZGcHIyAiMRiNYlkVOTg7CwsLwox/9CBkZGcjOzobFYkFvb68Am7y8PMhkMrz99tvgOA6rVq2CxWJBR0cHJicn6W+lsLAQkZGROHXqFDo7O/HAAw/AYrHAZrPB7XbD5XKBZVkUFxcjJiYG586dwwcffIDHH38cLS0taG5uhsfjwdjYGFiWhdlsRnx8PGw2G37xi19gz549GBkZgdVqxczMDIaHhwXYjI2N4Y033sCWLVuwsLAAi8UCh8NBxw3LskhPT8fi4iJeffVVrFq1iv5mh4eH6bgh2EgkEvz4xz9GSkoKDAYDrFYrenp6KDYsyyI/Px8ymQzvvPMO5ufnsWbNGoqN0+lEVFQUWJaFyWRCZGQkTp8+jba2tk966butYG5Vx7pxgb8GoAbLF/M6APs5jmvh5ZwAUMRx3DGGYfYB2M1x3EMMwxQC+BmWeQg9gA8AGADEA1i4MRlEAvgPAD/gOO70zY6lvLycu5220+985ztYtWoVNm/eDGB5RWq1WtHY2IipqSlERESgqKgIdXV1MBqN2LdvHwBgamoKjY2NsFgssNvtkMlkyM/PR3NzM5RKJZ599lkAyyuL5uZmWCwWDA0NISwsDAaDASMjI3C5XPRWb2FhATabDRaLBd3d3QCWV7CLi4vo7+/Hc889B6VSicXFRXR2dsJqtaK9vR1LS0vQ6XRISEhAc3MzDh48iOzsbHAch97eXlgsFrS2tmJhYQHx8fEwGAy4fPkytm3bhoqKCnAch5GREVgsFjQ1NWFubg4xMTEoLi7G+fPnUVVVha1btwJYXnVZrVZYrVaKjclkwpUrV5CTk4MDBw4AAKanpyk2ExMTkEqlyM/PR2trK2JiYvDcc89RbFpaWmCxWDA4OAiGYWAwGDA2Ngan0ynApq2tDRaLBdevXwewvEoDgN7eXjzzzDNISEjA4uIiurq66ES8tLQErVaLxMRENDU1Yf/+/TAYDOA4Dn19fXSyIdjk5ubi0qVL2LJlC6qrl/sY+Ni43W5ER0ejuLgYFy5cQEVFBbZt2wYAcDgcFBuXy4Xw8HCYTCbU19cjKysLjz76KMWmqakJFosF4+PjkEqlyMvLQ3t7OyIiIvDiiy8CADweD8VmYGAADMMgJycHdrsdDocDr7zyCsLCwrCwsID29nY6ERNswsLC0N3djePHjyMxMRFLS0sCbBYXF6HRaKDVamG1WvHwww8jLy8PHMehv79fsEhRqVTIz8/HhQsXsGnTJqxevZpiQ34rbrcbUVFRKC4uxsWLF1FaWor7778fwHIpjmDjdDoRHh6OwsJCXL16FRkZGXj88ccBLJelCDZjY2OQSCTIy8tDR0cHZDIZvva1r1FsWltbYbFY0N/fT7FxOp0YHx/H17/+dchkMvh8PgE2HMchLS0NMpkMXV1dOHbsGDQaDZaWlnD9+nU6ERNsdDodLBYL9u7di4KCAnAch4GBAVgsFjQ3N2N+fh5KpRKFhYU4f/48ampqsGbNGgD
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#2 Create mesh and define function space\n",
    "nx = 0.008\n",
    "ny = 0.003\n",
    "mesh = RectangleMesh(Point(0,0),Point(nx,ny),30, 30,'left')\n",
    "V = FunctionSpace(mesh, 'Lagrange', 1) #Lagrange are triangular elements\n",
    "plot(mesh)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Boundary conditions\n",
    "u0 = Constant(100)\n",
    "def boundary(x, on_boundary):\n",
    "    return on_boundary\n",
    "\n",
    "bc = DirichletBC(V,u0, boundary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calling FFC just-in-time (JIT) compiler, this may take some time.\n"
     ]
    }
   ],
   "source": [
    "u_n = project(1, V)\n",
    "u = TrialFunction(V)\n",
    "v = TestFunction(V)\n",
    "f = Constant(0.0)\n",
    "F = u*v*dx + alpha*dt*dot(grad(u), grad(v))*dx-u_n*v*dx\n",
    "a, L = lhs(F), rhs(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Calling FFC just-in-time (JIT) compiler, this may take some time.\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAD4CAYAAAAZ1BptAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJztvX2YZVV95/v5VnVX0w3Y7QXNSIORSYMJEDHKg+ZFrxFBdCI98WVoEl9DQp65EN/uzQ3MHdHxXueGjNFxMppMj2AYE3kJ6EyPGlGHJN5LtKF5UWkQb/OiNqgIQqtIv1X97h977+5du9Zea+1zzj51qvr3eZ56qs7ea++zzql91uf8fmvttWRmOI7jOE6IqcWugOM4jjO5uCQcx3GcVlwSjuM4TisuCcdxHKcVl4TjOI7TikvCcRzHacUl4TjOxCLpVElflvR1Sf9d0lNayr1N0p2Stkt6e+p4STOSPlZu/6qkl2TU5SJJOySZpKNH9iInHJeE4zgTgaSXSPrLxuaPAheb2S8CnwL+MHDcKcDvAacDpwK/IWlD4vjfAyi3nwn8qaRUe3gT8DLgWx1f2pLGJeE4ziRzIvCl8u8vAK8JlPkFYKuZ/dTM9gP/ALw6cfxJwI0AZvYw8DhwGoCks8ro4zZJfyPpiLLc7Wb2wChf3FLAJeE4ziSzHdhY/v064LhAmTuBF0k6StIa4JW1cm3HfxU4R9IKSccDzweOK9NI/xp4mZk9D9gGvHPEr2lJsWKxK+A4zqGNpK3AKuAI4H+SdEe564+A3wH+g6R3AVuAvc3jzexuSZcBnweeAO4AZsvdbcdfQRGBbKNIH/1jecwLKaKMmyQBzABfHuXrXWrI525yHGcSKDuP32xmb27ZfyLwV2Z2euI8/xbYaWYfyT1e0j8Cvwv8HPBbZnZe5PwPAKeZ2SPRF7RM8HST4zgTi6Snl7+nKNJAf5Eo90yK/ohPxI6XtEbS4eXfZwL7zewu4CvAr1Yd35IOL+VyyOKScBxnkjlP0jeBbwAPAR8DkHSMpM/Wyl0v6S7gvwMXmtnjseOBpwO3SbqbIq31BgAz+wHwZuAqSV+jSDX9fPmcb5W0EzgW+Jqkj/b0micKTzc5juM4rXgk4TiO47Tio5scx3ECnPnrq+3RH85llb39a3tvMLOze67SouCScBzHCfDoD+e46XPHZJVdc8wDy3aaDk83OY7jOK24JBzHccaApLMl3VNOEnhxYP8qSdeU+7dKelZt3yXl9nskvby2vevEhmdKurXcfqukl6bq7ZJwHMfpGUnTwIeBV1Dc0X2epJMaxc4HHjOzDcAHgcvKY08CNgEnA2cDH5E0PeDEho8Aryq3vwn4eKruLgnHcZz+OR3YYWb3mdle4GoOzilVsRG4svz7OuAMFXODbASuNrM9ZnY/sKM8X+eJDctJCh8qt28HVktaFau4d1w7juMEmMXYNbcnt/jRkrbVHm82s821x+uB79Qe7wRe0DjHgTJmtl/SLuCocvtXGseup5jY8H2SjgKepJjYsKpDNbHhf6V9YsTXALeZWfRFuiQcx3GG5xEzO22cTzjgxIYASDqZIp11Vup5PN3kOI7TPw8y/9v8seW2YBlJK4C1wKOxY83scjN7vpm9GHgM+Ga5/RtmdpaZPR+4Cri3OljSsRT9FG80s3tJ4JJwHMfpn1uAEyQdL2mGoiN6S6PMForOZIDXAjdaMW/SFmBTOfrpeOAE4GYYaGLDdcBnKDq1b8qpuKebHMdxeqbsY7gIuAGYBq4ws+2S3gtsM7MtwOXAxyXtAH5IIRLKctcCdwH7KSYwrNJK15d9EvtYOLHhheXfn+TgxIYXARuASyVdWm47q1ydL4hP8Oc4jhPglOfM2PWfybuR+uef+d1bx90nMS483eQ4juO04pJwHMdxWnFJOI7jOK24JBzHcZxWXBKO4zhOKz4E1nEcJ8As4vG56LRGhwQeSTiO4zituCQcx3GcVlwSjuM4TisuCcdxHKcV77h2HMcJsN+meHTu8MWuxqLjkYTjOI7TikvCcRzHacUl4TiO47TiknAcx3Fa8Y5rx3GcALNM8fisd1x7JOE4juO04pJwHMcZA5LOlnSPpB2SLg7sXyXpmnL/VknPqu27pNx+j6SX17a/TdKdkrZLentt+3skPSjpjvLnleX2MyXdKunr5e+Xpurt6SbHcZyekTQNfBg4E9gJ3CJpi5ndVSt2PvCYmW2QtAm4DDhX0kkU612fDBwDfFHSicAvAL8HnA7sBT4n6dNmtqM83wfN7P2NqjwCvMrMHpJ0CsWa2+tjdfdIwnEcp39OB3aY2X1mthe4GtjYKLMRuLL8+zrgDEkqt19tZnvM7H5gR3m+XwC2mtlPzWw/8A/Aq2OVMLPbzeyh8uF2YLWk6FS3LgnHcZzhOVrSttrPBY3964Hv1B7vZOE3+ANlykZ/F3BU5Ng7gRdJOkrSGuCVwHG1chdJ+pqkKyQ9NVDn1wC3mdme2AvzdJPjOE6AWZvi8dk1ucUfMbPT+qxPEzO7W9JlwOeBJ4A7gNly958D/ydg5e8/BX6nOlbSyRTprLNSz+ORhOM4Tv88yPxv+ceW24JlJK0A1gKPxo41s8vN7Plm9mLgMeCb5fbvm9msmc0B/5kiPUV57mOBTwFvNLN7UxV3STiO4/TPLcAJko6XNEPREb2lUWYL8Kby79cCN5qZlds3laOfjgdOAG4GkPT08vczKfojPlE+fkbtvL9JkZpC0jrgM8DFZnZTTsU93eQ4jtMzZrZf0kUUo4mmgSvMbLuk9wLbzGwLcDnwcUk7gB9SiISy3LXAXcB+4EIzq9JK10s6CthXbn+83P4nkp5LkW56APj9cvtFwAbgUkmXltvOMrOH2+quQlSO4zhOnZ895Uj7o+vzuhku/Pm/v3XcfRLjwiMJx3GcALNMsWt29WJXY9HxPgnHcRynFZeE4ziO04pLwnEcx2nFJeE4juO04h3XjuM4AfbbNI/t8/UkPJJwHMdxWnFJOI7jOK24JBzHcZxWXBKO4zhOKy4Jx3EcpxUf3eQ4jhNg1sSP9h+22NVYdDyScBzHcVpxSTiO4zituCQcx3GcVlwSjuM4Tivece04jhNgzqb4sXdceyThOI7jtJMlCUlnS7pH0g5JFwf2r5J0Tbl/q6Rn1fZdUm6/R9LLy22HSbpZ0lclbZf0b0b1ghzHcSaRUbej5fa3SbqzbEffXtv+unLbnKTTatvPlHSrpK+Xv1+aqndSEpKmgQ8DrwBOAs6TdFKj2PnAY2a2AfggcFl57EkUi3mfDJwNfKQ83x7gpWZ2KvBc4GxJL0zVxXEcZynSRzsq6RTg94DTgVOB35C0oTzXncCrgS81nuMR4FVm9ovAm4CPp+qeE0mcDuwws/vMbC9wNbCxUWYjcGX593XAGZJUbr/azPaY2f3ADuB0K/hJWX5l+WMZdXEcx1mKjLwdBX4B2GpmPzWz/cA/UIgBM7vbzO5pVsLMbjezh8qH24HVklbFKp7Tcb0e+E7t8U7gBW1lzGy/pF3AUeX2rzSOXQ8HzHorsAH4sJltDT25pAuACwAOX6Pnn7hhZUaVHcc5lLn9a3sfMbOnDXOOWRM/2RdtP+scLWlb7fFmM9tce9xHO3on8D5JRwFPAq8EtpHPa4DbzGxPrNCijW4ys1nguZLWAZ+SdIqZ3RkotxnYDPC8U1fZTZ87Zsw1nQx2zUX/j84hzNqp7IbskGHNMQ98a8xP+YiZnZYuNjrM7G5JlwGfB54A7gBmc46VdDJFOuusVNkcSTwIHFd7fGy5LVRmp6QVwFrg0ZxjzexxSX9HkWtbIIlJYBIb6F1zi10DZ7FZWyaLJ+36dGkF6aUdNbPLgcsBJP1biigjiqRjgU8BbzSze1PlcyRxC3CCpOPLim0CfqtRZgtFJ8iXgdcCN5qZSdoCfELSB4BjgBOAmyU9DdhXCmI1cCZlJ8246fMDNu6G/PE5/3AeCqybKq7ZcV1fazsOlO/ymTqEhDLydhRA0tPN7GFJz6Toj4gOACozN58BLjazm3IqnpREmRu7CLgBmAauMLP
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = Function(V)\n",
    "t = 0\n",
    "for n in range(num_steps):\n",
    "    t += dt\n",
    "    #u0.t = t\n",
    "    solve(a == L, u, bc)\n",
    "    c = plot(u,)\n",
    "    plt.colorbar(c)\n",
    "    plt.show()\n",
    "    u_n.assign(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-07"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1E-7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100.0000001"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1E-7+1e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}