{
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"colab": {
"name": "902_Poisson Equation-Zero Boundary Conditions.ipynb",
"provenance": [],
"include_colab_link": true
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"cells": [
{
"cell_type": "markdown",
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"id": "view-in-github",
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"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9zTPh0YzDl0T"
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"source": [
"# Finite Difference Methods for the Poisson Equation with Zero Boundary\n",
"This notebook will focus on numerically approximating a inhomogenous second order Poisson Equation with zero boundary conditions.\n",
"## The Differential Equation\n",
"The general two dimensional Poisson Equation is of the form:\n",
"\\begin{equation} \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=f(x,y), \\ \\ \\ (x,y) \\in \\Omega=(0,1)\\times (0,1),\\end{equation}\n",
"with boundary conditions\n",
"\\begin{equation}U(x,y) = g(x,y), \\ \\ \\ (x,y)\\in\\delta\\Omega\\text{ - boundary}. \\end{equation}\n",
"## Homogenous Poisson Equation\n",
"This notebook will implement a finite difference scheme to approximate the inhomogenous form of the Poisson Equation $f(x,y)=x^2+y^2$, with a zero boundary:\n",
"\\begin{equation} \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=x^2+y^2.\\end{equation}\n",
"with the Boundary Conditions:\n",
"\\begin{equation} u(x,0)=0, \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ lower},\\end{equation}\n",
"\\begin{equation} u(x,1)=0, \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ upper},\\end{equation}\n",
"\\begin{equation} u(0,y)=0, \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ left},\\end{equation}\n",
"\\begin{equation} u(1,y)=0, \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ right}.\\end{equation}\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "cubPfK4IDl0W"
},
"source": [
"# LIBRARY\n",
"# vector manipulation\n",
"import numpy as np\n",
"# math functions\n",
"import math \n",
"\n",
"# THIS IS FOR PLOTTING\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt # side-stepping mpl backend\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"from IPython.display import HTML\n",
"from mpl_toolkits.mplot3d import axes3d\n",
"import matplotlib.pyplot as plt\n"
],
"execution_count": 1,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "JvwVxSKkDl0Y"
},
"source": [
"## Discete Grid\n",
"The region $\\Omega=(0,1)\\times(0,1)$ is discretised into a uniform mesh $\\Omega_h$. In the $x$ and $y$ directions into $N$ steps giving a stepsize of\n",
"\\begin{equation} h=\\frac{1-0}{N},\\end{equation}\n",
"resulting in \n",
"\\begin{equation}x[i]=0+ih, \\ \\ \\ i=0,1,...,N,\\end{equation}\n",
"and \n",
"\\begin{equation}x[j]=0+jh, \\ \\ \\ j=0,1,...,N,\\end{equation}\n",
"The Figure below shows the discrete grid points for $N=10$, the known boundary conditions (green), and the unknown values (red) of the Poisson Equation."
]
},
{
"cell_type": "code",
"metadata": {
"id": "xHLmkY9gDl0Y",
"outputId": "69afb3e5-0070-4b4c-e6f5-46b808d407ca",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 324
}
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"source": [
"N=10\n",
"h=1/N\n",
"x=np.arange(0,1.0001,h)\n",
"y=np.arange(0,1.0001,h)\n",
"X, Y = np.meshgrid(x, y)\n",
"fig = plt.figure()\n",
"plt.plot(x[1],y[1],'ro',label='unknown');\n",
"plt.plot(X,Y,'ro');\n",
"plt.plot(np.ones(N+1),y,'go',label='Boundary Condition');\n",
"plt.plot(np.zeros(N+1),y,'go');\n",
"plt.plot(x,np.zeros(N+1),'go');\n",
"plt.plot(x, np.ones(N+1),'go');\n",
"plt.xlim((-0.1,1.1))\n",
"plt.ylim((-0.1,1.1))\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.gca().set_aspect('equal', adjustable='box')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
"plt.title(r'Discrete Grid $\\Omega_h,$ h= %s'%(h),fontsize=24,y=1.08)\n",
"plt.show();"
],
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "cP4exvczDl0Z"
},
"source": [
"## Boundary Conditions\n",
"\n",
"The discrete boundary conditions are \n",
"\\begin{equation} w[i,0]=0, \\text{ for } i=0,...,10, \\text{ upper},\\end{equation} \n",
"\\begin{equation} w[i,N]=0, \\text{ for } i=0,...,10, \\text{ lower},\\end{equation}\n",
"\\begin{equation} w[0,j]=0, \\text{ for } j=0,...,10, \\text{ left},\\end{equation}\n",
"\\begin{equation} w[N,j]=0, \\text{ for } i=0,...,10,\\text{ right}. \\end{equation}\n",
"\n",
"The Figure below plots the boundary values of $w[i,j]$."
]
},
{
"cell_type": "code",
"metadata": {
"id": "_HZhuy_6Dl0a",
"outputId": "4ed35e9f-4316-4f6a-8023-a7d1d48255a6",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 272
}
},
"source": [
"w=np.zeros((N+1,N+1))\n",
"\n",
"for i in range (0,N):\n",
" w[i,0]=0 #left Boundary\n",
" w[i,N]=0 #Right Boundary\n",
"\n",
"for j in range (0,N):\n",
" w[0,j]=0 #Lower Boundary\n",
" w[N,j]=0 #Upper Boundary\n",
"\n",
" \n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"# Plot a basic wireframe.\n",
"ax.plot_wireframe(X, Y, w,color='r', rstride=10, cstride=10)\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('y')\n",
"ax.set_zlabel('w')\n",
"plt.title(r'Boundary Values',fontsize=24,y=1.08)\n",
"plt.show()"
],
"execution_count": 3,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
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"cell_type": "markdown",
"metadata": {
"id": "9A5FZA51Dl0b"
},
"source": [
"## Numerical Method\n",
"The Poisson Equation is discretised using \n",
"$\\delta_x^2$ is the central difference approximation of the second derivative in the $x$ direction\n",
"\\begin{equation}\\delta_x^2=\\frac{1}{h^2}(w_{i+1j}-2w_{ij}+w_{i-1j}), \\end{equation}\n",
"and $\\delta_y^2$ is the central difference approximation of the second derivative in the $y$ direction\n",
"\\begin{equation}\\delta_y^2=\\frac{1}{h^2}(w_{ij+1}-2w_{ij}+w_{ij-1}). \\end{equation}\n",
"The gives the Poisson Difference Equation,\n",
"\\begin{equation}-(\\delta_x^2w_{ij}+\\delta_y^2w_{ij})=f_{ij} \\ \\ (x_i,y_j) \\in \\Omega_h, \\end{equation}\n",
"\\begin{equation}w_{ij}=g_{ij} \\ \\ (x_i,y_j) \\in \\partial\\Omega_h, \\end{equation}\n",
"where $w_ij$ is the numerical approximation of $U$ at $x_i$ and $y_j$.\n",
"Expanding the the Poisson Difference Equation gives the five point method,\n",
"\\begin{equation}-(w_{i-1j}+w_{ij-1}-4w_{ij}+w_{ij+1}+w_{i+1j})=h^2f_{ij} \\end{equation}\n",
"for $i=1,...,N-1$ and $j=1,...,N-1.$\n",
"\n",
"### Matrix form\n",
"This can be written as a system of $(N-1)\\times(N-1)$ equations can be arranged in matrix form\n",
"\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n",
"where $A$ is an $(N-1)^2\\times(N-1)^2$ matrix made up of the following block tridiagonal structure\n",
"\\begin{equation}\\left(\\begin{array}{ccccccc}\n",
"T&I&0&0&.&.&.\\\\\n",
"I&T&I&0&0&.&.\\\\\n",
".&.&.&.&.&.&.\\\\\n",
".&.&.&0&I&T&I\\\\\n",
".&.&.&.&0&I&T\\\\\n",
"\\end{array}\\right),\n",
"\\end{equation}\n",
"where $I$ denotes an $N-1 \\times N-1$ identity matrix and $T$ is the tridiagonal matrix of the form:\n",
"\\begin{equation} T=\\left(\\begin{array}{ccccccc}\n",
"-4&1&0&0&.&.&.\\\\\n",
"1&-4&1&0&0&.&.\\\\\n",
".&.&.&.&.&.&.\\\\\n",
".&.&.&0&1&-4&1\\\\\n",
".&.&.&.&0&1&-4\\\\\n",
"\\end{array}\\right).\n",
"\\end{equation}\n",
"The plot below shows the matrix $A$ and its inverse $A^{-1}$ as a colourplot."
]
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"id": "GSQs_RjiDl0b",
"outputId": "820ebd91-4f4d-4739-8db6-69b408bdae51",
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"source": [
"N2=(N-1)*(N-1)\n",
"A=np.zeros((N2,N2))\n",
"## Diagonal \n",
"for i in range (0,N-1):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j]=-4\n",
"\n",
"# LOWER DIAGONAL \n",
"for i in range (1,N-1):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j-1]=1 \n",
"# UPPPER DIAGONAL \n",
"for i in range (0,N-2):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j+1]=1 \n",
"\n",
"# LOWER IDENTITY MATRIX\n",
"for i in range (0,N-1):\n",
" for j in range (1,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*(j-1)]=1 \n",
" \n",
" \n",
"# UPPER IDENTITY MATRIX\n",
"for i in range (0,N-1):\n",
" for j in range (0,N-2): \n",
" A[i+(N-1)*j,i+(N-1)*(j+1)]=1\n",
"Ainv=np.linalg.inv(A) \n",
"fig = plt.figure(figsize=(12,4));\n",
"plt.subplot(121)\n",
"plt.imshow(A,interpolation='none');\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"plt.title('Matrix A ',fontsize=24)\n",
"plt.subplot(122)\n",
"plt.imshow(Ainv,interpolation='none');\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"plt.title(r'Matrix $A^{-1}$ ',fontsize=24)\n",
"\n",
"fig.tight_layout()\n",
"plt.show();"
],
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Xd68a9mmDl0d"
},
"source": [
"\n",
"\n",
"The vector $\\mathbf{w}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors $\\mathbf{w}_j$ of length $N-1$ of the form\n",
"\\begin{equation}\\mathbf{w}_j=\\left(\\begin{array}{c}\n",
"w_{1j}\\\\\n",
"w_{2j}\\\\\n",
".\\\\\n",
".\\\\\n",
"w_{N-2j}\\\\\n",
"w_{N-1j}\\\\\n",
"\\end{array}\\right).\n",
"\\end{equation}\n",
"The vector $\\mathbf{r}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors of the form $\\mathbf{r}_j=-h^2\\mathbf{f}_j-\\mathbf{bx}_{j}-\\mathbf{by}_j$. In this example the boundary is $0$ which means that\n",
"\\begin{equation}\\mathbf{bx}_j =0,\\end{equation}\n",
"\\begin{equation}\n",
"\\mathbf{by}_{j} =0,\n",
"\\end{equation}\n",
"and \n",
"\\begin{equation}\\mathbf{f}_j =\\left(\\begin{array}{c}\n",
"x_1^2+y_j^2\\\\\n",
"x_2^2+y_j^2\\\\\n",
".\\\\\n",
".\\\\\n",
"x_{N-2}^2+y_j^2\\\\\n",
"x_{N-1}^2+y_j^2\\\\\n",
"\\end{array}\\right)\n",
"\\end{equation}\n",
"for $j=1,...,N-1$.\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "lsE1goP_Dl0d"
},
"source": [
"r=np.zeros(N2)\n",
"\n",
"# vector r \n",
"for i in range (0,N-1):\n",
" for j in range (0,N-1): \n",
" r[i+(N-1)*j]=h*h*(x[i]*x[i]+y[j]*y[j]) \n",
"# Boundary \n",
"b_bottom_top=np.zeros(N2)\n",
"for i in range (0,N-1):\n",
" b_bottom_top[i]=0 #Bottom Boundary\n",
" b_bottom_top[i+(N-1)*(N-2)]=0# Top Boundary\n",
" \n",
"b_left_right=np.zeros(N2)\n",
"for j in range (0,N-1):\n",
" b_left_right[(N-1)*j]=0 # Left Boundary\n",
" b_left_right[N-2+(N-1)*j]=0# Right Boundary\n",
" \n",
"b=b_left_right+b_bottom_top"
],
"execution_count": 5,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "d--unX_YDl0e"
},
"source": [
"## Results\n",
"\n",
"To solve the system for $\\mathbf{w}$ invert the matrix $A$\n",
"\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n",
"such that\n",
"\\begin{equation} \\mathbf{w}=A^{-1}\\mathbf{r}.\\end{equation}\n",
"Lastly, as $\\mathbf{w}$ is in vector it has to be reshaped into grid form to plot.\n",
"\n",
"The figure below shows the numerical approximation of the homogeneous Equation."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "zWPBvj0dDl0f",
"outputId": "9e0c29b9-e14b-413b-e0f9-145a6ed09445",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 380
}
},
"source": [
"C=np.dot(Ainv,r-b)\n",
"w[1:N,1:N]=C.reshape((N-1,N-1))\n",
"\n",
"fig = plt.figure(figsize=(8,6))\n",
"ax = fig.add_subplot(111, projection='3d');\n",
"# Plot a basic wireframe.\n",
"ax.plot_wireframe(X, Y, w,color='r');\n",
"ax.set_xlabel('x');\n",
"ax.set_ylabel('y');\n",
"ax.set_zlabel('w');\n",
"plt.title(r'Numerical Approximation of the Poisson Equation',fontsize=24,y=1.08);\n",
"plt.show();"
],
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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"text/plain": [
""
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"# Consistency and Convergence\n",
"We now ask how well the grid function determined by the five point scheme approximates the exact solution of the Poisson problem.\n",
"## Consistency\n",
"\n",
"### Consitency (Definition)\n",
"Let \n",
"\\begin{equation}\\nabla^2_h(\\varphi)=-(\\varphi_{i-1j}+\\varphi_{ij-1}-4\\varphi_{ij}+\\varphi_{ij+1}+\\varphi_{i+1j})\\end{equation} \n",
"denote the finite difference approximation associated with the grid $\\Omega_h$ having the mesh size $h$, to a partial differential operator \n",
"\\begin{equation}\\nabla^2(\\varphi)=\\frac{\\partial^2 \\varphi}{\\partial x^2}+\\frac{\\partial^2 \\varphi}{\\partial y^2}\\end{equation} defined on\n",
"a simply connected, open set $\\Omega \\subset R^2$. For a given function $\\varphi\\in C^{\\infty}(\\Omega)$,\n",
"the truncation error of $\\nabla^2_h$ is\n",
"\\begin{equation}\\tau_{h}(\\mathbf{x})=(\\nabla^2-\\nabla^2_h)\\varphi(\\mathbf{x}) \\end{equation}\n",
"The approximation $\\nabla^2_h$ is consistent with $\\nabla^2$ if\n",
"\\begin{equation}\\lim_{h\\rightarrow 0}\\tau_h(\\mathbf{x})=0,\\end{equation}\n",
"for all $\\mathbf{x} \\in D$ and all $\\varphi \\in C^{\\infty}(\\Omega)$. The approximation is consistent to order $p$ if $\\tau_h(\\mathbf{x})=O(h^p)$.\n",
"\n",
"_In other words a method is consistent with the differential equation it is approximating._\n",
"\n",
"## Proof of Consistency\n",
"The five-point difference analog $\\nabla^2_h$ is consistent to order 2 with $\\nabla^2$.\n",
"\n",
"__Proof__\n",
"\n",
"Pick $\\varphi \\in C^{\\infty}(D)$, and let $(x,y) \\in \\Omega$ be a point such that $(x\\pm h, y),(x,y \\pm h) \\in \\Omega\\bigcup \\partial\\Omega$. By the Taylor Theorem\n",
"\\begin{eqnarray*}\n",
"\\varphi(x\\pm h,y)&=&\\varphi(x,y) \\pm h \\frac{\\partial \\varphi}{\\partial x}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y) \\pm\\frac{h^3}{3!}\\frac{\\partial^3 \\varphi}{\\partial x^3}(x,y)+\\frac{h^4}{4!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{\\pm},y)\n",
"\\end{eqnarray*}\n",
"where $\\zeta^{\\pm} \\in (x-h,x+h)$. Adding this pair of equation together and rearranging , we get\n",
"\\begin{equation}\\frac{1}{h^2}[\\varphi(x+h,y)-2\\varphi(x,y)+\\varphi(x-h,y) ] -\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)=\\frac{h^2}{4!}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n",
"\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n",
" \\right]\n",
"\\end{equation}\n",
"By the intermediate value theorem\n",
"\\end{equation}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n",
"\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n",
" \\right]\n",
"=2\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y),\\end{equation}\n",
"for some $\\zeta \\in (x-h,x+h)$. Therefore,\n",
"\\begin{equation}\\delta_x^2(x,y)\n",
"=\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y)\\end{equation}\n",
"Similar reasoning shows that\n",
"\\begin{equation}\\delta_y^2(x,y)\n",
"=\\frac{\\partial^2 \\varphi}{\\partial y^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial y^4}(x,\\eta)\n",
"\\end{equation}\n",
"for some $\\eta \\in (y-h,y+h)$. We conclude that $\\tau_h(x,y)=(\\nabla-\\nabla_h)\\varphi(x,y)=O(h^2).$\n",
"\n"
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"## Convergence\n",
"### Definition\n",
"Let $\\nabla^2_hw(\\mathbf{x}_j)=f(\\mathbf{x}_j)$ be a finite difference approximation, defined on a grid mesh size $h$, to a PDE $\\nabla^2U(\\mathbf{x})=f(\\mathbf{x})$ on a simply connected set $D \\subset R^n$. Assume that $w(x,y)=U(x,y)$ at all points $(x,y)$ on the boundary $\\partial\\Omega$. The finite difference scheme converges (or is convergent) if\n",
"\\end{equation} \\max_j|U(\\mathbf{x}_j)-w(\\mathbf{x}_j)| \\rightarrow 0 \\mbox{ as } h \\rightarrow 0.\\end{equation}\n"
]
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"### Theorem (DISCRETE MAXIMUM PRINCIPLE).\n",
"If $\\nabla^2_hV_{ij}\\geq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n",
"\\begin{equation} \\max_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\leq \\max_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij},\\end{equation}\n",
"If $\\nabla^2_hV_{ij}\\leq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n",
"\\begin{equation} \\min_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\geq \\min_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij}.\\end{equation}"
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"### Propositions\n",
"1. The zero grid function for which $U_{ij}=0$ for all $(x_i,y_j) \\in \\Omega_h \\bigcup \\partial\\Omega_h$\n",
"is the only solution to the finite difference problem\n",
"\\begin{equation}\\nabla_h^2U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n",
"\\begin{equation}U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n",
"\n",
"2. For prescribed grid functions $f_{ij}$ and $g_{ij}$, there exists a unique solution to the problem\n",
"\\begin{equation}\\nabla_h^2U_{ij}=f_{ij} \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n",
"\\begin{equation}U_{ij}=g_{ij} \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n"
]
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"### Definition\n",
"For any grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h \\rightarrow R$,\n",
"\\begin{equation}||V||_{\\Omega} =\\max_{(x_i,y_j)\\in\\Omega_h}|V_{ij}|, \\end{equation}\n",
"\\begin{equation}||V||_{\\partial\\Omega} =\\max_{(x_i,y_j)\\in\\partial\\Omega_h}|V_{ij}|. \\end{equation}\n",
"\n",
"### Lemma\n",
"If the grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h\\rightarrow R$ satisfies the boundary condition $V_{ij}=0$ for $(x_i,y_j)\\in \\partial\\Omega_h$, then\n",
"\\begin{equation}||V_||_{\\Omega}\\leq \\frac{1}{8}||\\nabla_h^2V||_{\\Omega}. \\end{equation}"
]
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"Given these Lemmas and Propositions, we can now prove that the solution to the five point scheme $\\nabla^2_h$ is convergent to the exact solution of the Poisson Equation $\\nabla^2$.\n",
"### Convergence Theorem\n",
"Let $U$ be a solution to the Poisson equation and let $w$ be the grid function\n",
"that satisfies the discrete analog\n",
"\\begin{equation}-\\nabla_h^2w_{ij}=f_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\Omega_h, \\end{equation}\n",
"\\begin{equation}w_{ij}=g_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\partial\\Omega_h. \\end{equation}\n",
"Then there exists a positive constant $K$ such that\n",
"\\begin{equation}||U-w||_{\\Omega}\\leq KMh^2, \\end{equation}\n",
"where\n",
"\\begin{equation} M=\\left\\{\n",
"\\left|\\left|\\frac{\\partial^4 U}{\\partial x^4} \\right|\\right|_{\\infty},\n",
"\\left|\\left|\\frac{\\partial^4 U}{\\partial y^4} \\right|\\right|_{\\infty}\n",
" \\right\\}\\end{equation}\n",
" \n",
" __Proof__\n",
" \n",
" The statement of the theorem assumes that $U\\in C^4(\\bar{\\Omega})$. This assumption\n",
"holds if $f$ and $g$ are smooth enough.\n",
"\\begin{proof}\n",
"Following from the proof of the Proposition we have\n",
"\\begin{equation} (\\nabla_h^2-\\nabla^2)U_{ij}=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right],\\end{equation}\n",
"for some $\\zeta \\in (x_{i-1},x_{i+1})$ and $\\eta_j\\in(y_{j-1},y_{j+1})$. Therefore,\n",
"\\begin{equation} -\\nabla_h^2U_{ij}=f_{ij}-\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n",
"If we subtract from this the identity equation $-\\nabla_h^2w_{ij}=f_{ij}$ and note\n",
"that $U-w$ vanishes on $\\partial\\Omega_h$, we find that\n",
"\\begin{equation} \\nabla_h^2(U_{ij}-w_{ij})=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n",
"It follows that\n",
"\n",
"\\begin{equation} ||U-w||_{\\Omega}\\leq\\frac{1}{8}||\\nabla_h^2(U-w)||_{\\Omega}\\leq KMh^2.\\end{equation}"
]
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