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"---\n",
"title: \"Galerkin Method and Finite Elements\"\n",
"subtitle: \"Lecture 16\"\n",
"date: 2026-04-08\n",
"abstract-title: Overview\n",
"format:\n",
" html:\n",
" other-links:\n",
" - text: This notebook\n",
" href: L16.ipynb\n",
"---"
]
},
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"::: {.callout-note}\n",
"\n",
"I encourage you to play around with the juptyer notebook for this lecture - you can copy the code with the ```this notebook``` button on the side of this page.\n",
"\n",
":::\n",
"\n",
"::: {.callout-warning}\n",
"\n",
"These notes are mainly a record of what we discussed and are not a substitute for attending the lectures and reading books! If anything is unclear/wrong, let me know and I will update the notes.\n",
"\n",
":::\n",
"\n",
"::: {.callout-tip}\n",
"\n",
"This chapter is mostly based on \n",
"\n",
"* @Burden Chapter 11, \n",
"* @FNC Chapter 10, \n",
"* Today: @FNC [Galerkin method](https://fncbook.com/galerkin/)\n",
"\n",
":::"
]
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"#| echo: false\n",
"\n",
"using Plots, LaTeXStrings, LinearAlgebra, Interpolations, SparseArrays\n",
"\n",
"# IF YOU ARE READING THIS, THANK YOU\n",
"# FOR DOWNLOADING THE LECTURE NOTES.\n",
"# THE FIRST PERSON TO LET ME KNOW,\n",
"# WINS SOME CHOCOLATES OF YOUR CHOICE"
]
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"source": [
"## Recap\n",
"\n",
"We are considering linear boundary value problems of the following form: \n",
"\n",
"\\begin{align}\n",
" \\mathcal L[u] &:= -u'' + p u' + q u = f &&\\text{on } (a,b) \\nonumber\\\\\n",
" &u(a)=0, \\qquad u(b) = 0 .\n",
" \\tag{BVP}\n",
"\\end{align}\n",
"\n",
"where $p, q$ may be functions of $x$. We will see that including non-zero boundary conditions is easy (as in the case of finite differences). By approximating the continuous problem with finite differences, we obtained a discrete problem: find $U \\in \\mathbb R^{n+1}$ (with index starting at $0$) such that \n",
"\n",
"\\begin{align}\n",
" \\begin{split}\n",
" &\\mathcal L_h [U] = F \\\\\n",
" &U_0 = U_n = 0 \n",
" \\end{split}\\tag{$\\text{BVP}_h$}\n",
"\\end{align}\n",
"\n",
"where $\\mathcal L_h$ depends on the choice of finite difference scheme. Here is the implementation we saw last time:"
]
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"\"\"\"\n",
" fdm(n, p, q, f; a=0,b=1, A=0,B=0)\n",
"\n",
"Approximate the solution to \n",
" -u′′ + p u′ + q u = 0 on (a,b)\n",
" u(a) = A, u(b) = B\n",
"using central finite differences\n",
"\"\"\"\n",
"function fdm(n, p, q, f; a=0.,b=1., A=0.,B=0.)\n",
" # mesh size\n",
" h = (b-a)/n \n",
" # interior grid points \n",
" x = [ a + j *(b-a)/n for j ∈ 1:n-1 ] \n",
"\n",
" # Finite Difference Coefficients\n",
" # (using a second order central difference) \n",
" d = (2/h^2) * ones(n-1) + q.(x)\n",
" d₋ = (-1/h^2)*ones(n-2) - p.(x[2:end])/(2h)\n",
" d₊ = (-1/h^2)*ones(n-2) + p.(x[1:end-1])/(2h)\n",
" Lh = Tridiagonal(d₋, d, d₊)\n",
" F = f.(x)\n",
" F[1] += (1/h^2 + p(x[1])/(2h))*A\n",
" F[end] += (1/h^2 - p(x[end])/(2h))*B\n",
" U = Lh \\ F\n",
"\n",
" # add the boundary conditions\n",
" x = [a, x..., b]\n",
" U = [A, U..., B]\n",
"\n",
" return x, U\n",
"end;"
]
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"source": [
"Today, we will look at an alternative approach involving approximating integrals instead of derivatives."
]
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"## Galerkin Method\n",
"\n",
"The content of this lecture is mainly contained in @FNC [Galerkin method](https://fncbook.com/galerkin/).\n",
"\n",
"We will consider second order linear equations but now written in a slightly different form (that will be more convenient for us):\n",
"\n",
"::: {#exr-}\n",
"\n",
"Show that we can write $-u'' + p u' + q u = g$ as $-(\\alpha u')' + \\beta u = f$ for some $\\alpha, \\beta, f$ depending on $p,q,g$.\n",
"\n",
"Hint: Use the integrating factor $e^z$ where $z$ is a function with $z' = -p$.\n",
"\n",
":::\n",
"\n",
"For the rest of this lecture, we will consider: For fixed data $\\alpha,\\beta,f$, find $u$ such that\n",
"\n",
"\\begin{align}\n",
" &- (\\alpha u')' + \\beta u = f \\qquad \\text{on } (a,b) \\nonumber\\\\\n",
" &u(a) = 0, \\quad u(b) = 0. \\tag{BVP}\n",
"\\end{align}\n",
"\n",
"We assume that $\\alpha$ has a continuous derivative, $\\alpha(x)\\geq c>0$, $\\beta$ is continuous with $\\beta(x) \\geq 0$, and $f$ is square integrable $\\int_a^b |f|^2 < \\infty$. \n",
"\n",
"### Weak formulation\n",
"\n",
"Notice that, if $u$ solves (BVP) and $v$ is a smooth function with $v(a) = v(b) = 0$, then multiplying (BVP) by $v$ and integrating, we have\n",
"\n",
"\\begin{align}\n",
" (f,v) &:= \\int_a^b f v \\nonumber\\\\\n",
" &= \\int_a^b \\left[ \n",
" - (\\alpha u')' + \\beta u\n",
" \\right] v \\, \\mathrm{d}x \\nonumber\\\\\n",
" %\n",
" &= - \\alpha(x) u'(x) v(x) \\Big|_a^b \\nonumber\\\\\n",
" %\n",
" &\\qquad + \\int_a^b \\left[ \n",
" \\alpha(x) u'(x) v'(x) + \\beta(x) u(x)v(x)\n",
" \\right] \\mathrm{d}x \n",
" \\nonumber\\\\\n",
" %\n",
" &= \\int_a^b \\left[ \n",
" \\alpha(x) u'(x) v'(x) + \\beta(x) u(x) v(x)\n",
" \\right] \\mathrm{d}x \\nonumber\\\\\n",
" %\n",
" &=: \\mathcal A(u,v).\n",
"\\end{align}\n",
"\n",
"Here, we have integrated by parts in the first term.\n",
"\n",
"We will let $V$ be a space of functions $v$ satisfying the boundary conditions $v(a) = v(b) = 0$ and for which we can define $\\mathcal A(u,v)$ for all $u,v \\in V$ (it takes a bit more work to define exactly what we mean by $V$ - see a course including Sobolev spaces - it is some space that includes smooth funcions satisfying the boundary conditions).\n",
"\n",
"The *weak formulation* of the problem can be written as: seek $u\\in V$ such that \n",
"\n",
"\\begin{align}\n",
" \\mathcal A(u, v) = (f, v) \\tag{weak}\n",
"\\end{align}\n",
"\n",
"for all $v\\in V$.\n",
"\n",
"::: {#exr-}\n",
"\n",
"Take $u,v, w\\in V$ and $\\lambda\\in\\mathbb R$. Explain why $\\mathcal A$ is \n",
"\n",
"* Positive: $\\mathcal A(u,u) \\geq 0$, \n",
"* Symmetric: $\\mathcal A(u,v) = \\mathcal A(v,u)$, \n",
"* Bilinear: $\\mathcal A(u+ \\lambda w,v) = \\mathcal A(u,v) + \\lambda\\mathcal A(w,v)$ and $\\mathcal A(u, v+\\lambda w) = \\mathcal A(u,v) + \\lambda\\mathcal A(u,w)$, \n",
"\n",
":::\n",
"\n",
"### Aside: Rayleigh-Ritz Approach \n",
"\n",
"::: {#exr-}\n",
"\n",
"Explain why minimising $I(u) := \\frac{1}{2} \\mathcal A(u,u) - (f,u)$ over $u \\in V$ is equivalent to solving $\\mathcal A(u,v) = (f,v)$ for all $v\\in V$.\n",
"\n",
"Hint: If $u$ is a minimiser and $v\\in V$, then\n",
"\n",
"\\begin{align}\n",
" I(u) &\\leq I(u + \\lambda v) \\nonumber\\\\\n",
" %\n",
" &= \\frac12 \\mathcal A(u + \\lambda v, u + \\lambda v) - (f,u + \\lambda v) \\nonumber\\\\\n",
" %\n",
" &= I(u) + \\lambda[\\mathcal A(u,v) - (f,v)] + \\frac{\\lambda^2}{2} \\mathcal A(v,v)\n",
"\\end{align}\n",
"\n",
"Explain why this means that $\\mathcal A(u,v)=(f,v)$. [this is the Euler-Lagrange equation (first order condition) for the minimisation problem].\n",
"\n",
":::\n",
"\n",
"### Galerkin approach \n",
"\n",
"The idea behind the Galerkin method is to solve $\\mathcal A(u,v) = (f,v)$ over a finite dimensional space of functions $V_h := \\mathrm{span}\\{\\phi_1,\\dots,\\phi_m\\}$:\n",
"\n",
"\\begin{align}\n",
" V_h = \\left\\{ v_h = \\sum_{j=1}^m c_j \\phi_j : c_j \\in \\mathbb R\\right\\}\n",
"\\end{align}\n",
"\n",
"($V_h$ is the space spanned by all linear combinations of the $\\phi_j$). Later, $h$ will denote the spacing of a grid but for now $h$ just means that $V_h$ is any discretisation of the problem.\n",
"\n",
"That is, we are considering the problem: Find $u \\in V_h$ such that $\\mathcal A(u,v) = (f,v)$ for all $v \\in V_h$. \n",
"\n",
"::: {#exr-}\n",
"\n",
"Explain why this problem is equivalent to: Find $u \\in V_h$ such that $\\mathcal A(u,\\phi_i) = (f,\\phi_i)$ for all $i=1,\\dots,m$.\n",
"\n",
":::\n",
"\n",
"Since, we are considering $u \\in V_h$, we may write \n",
"\n",
"\\begin{align}\n",
" u(x) = \\sum_{j=1}^m u_j \\phi_j(x).\n",
"\\end{align}\n",
"\n",
"Since $\\mathcal A$ is linear in the first component, we want to solve\n",
"\n",
"\\begin{align}\n",
" \\mathcal A(u, \\phi_i) = \\sum_{j=1}^m u_j \\mathcal A(\\phi_j,\\phi_i)\n",
" %\n",
" = (f,\\phi_i) \n",
"\\end{align}\n",
"\n",
"for all $i = 1,\\dots,m$.\n",
"\n",
"::: {#exr-}\n",
"\n",
"Show that this can be written as the matrix equation\n",
"\n",
"\\begin{align}\n",
" &Au = F \\qquad \\text{where} \\nonumber\\\\\n",
" &A_{ij} := \\mathcal A(\\phi_i,\\phi_j), \\quad F_i := (f,\\phi_i). \\nonumber\n",
"\\end{align} \n",
"\n",
":::\n",
"\n",
"As a result, we have \n",
"\n",
"\\begin{align}\n",
" A_{ij} &= K_{ij} + M_{ij} \\nonumber\\\\\n",
" K_{ij} &= \\int_a^b \n",
" \\alpha(x) \\phi_i'(x) \\phi_j'(x) \\, \\mathrm{d}x \\nonumber\\\\\n",
" %\n",
" M_{ij} &= \\int_{a}^b \\beta(x) \\phi_i(x) \\phi_j(x) \\, \\mathrm{d}x\n",
"\\end{align}\n",
"\n",
"$K$ is known as the *stiffness* matrix and $M$ is the *mass* matrix.\n",
"\n",
"As a result, we have taken the continuous problem (find $u\\in V$ such that $\\mathcal A(u,v) = (f,v)$ for all $v\\in V$) and approximated it by a discrete problem (find $u\\in V_h$ such that $\\mathcal A(u,v) = (f,v)$ for all $v\\in V_h$) that can be written as linear system of equations $Au = F$. Since we are now in \"Linear Algebra World\", we can use results from Chapter 2: Iterative Methods (and last semester Chapter 5: Direct Methods) to solve this system of equations. "
]
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"### Finite elements\n",
"\n",
"In order to approximate the solution of $-(\\alpha u')' + \\beta u = f$, \"all\" we have to do is *(i)* choose a space $V_h$, *(ii)* build the matrices $K, M$ and the vector $F$, and *(iii)* solve a linear system of equations. \n",
"\n",
"**Step 1.** The finite element method involves choosing $V_h$ to be a space of peicewise polynomials (splines) defined relative to some *mesh*. The simplest possible choice are piecewise linear functions defined on the equispaced grid $x_j = a + jh := a + j\\frac{b-a}{n}$ for $j=0,\\dots,n$. We define $\\phi_i$ to be linear on each $I_j := [x_{j-1},x_j]$ and *cardinal*: $\\phi_i(x_i) = 1$ and $\\phi_i(x_j) = 0$ for all $j\\not=i$.\n",
"\n",
"::: {#exr-}\n",
"\n",
"Write down the definition of $\\phi_j(x)$.\n",
"\n",
":::\n",
"\n",
"Here's a plot of a couple of these functions:"
]
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{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a, b, n = 0, 1, 5 \n",
"h = (b-a)/n\n",
"# mesh: x_1, ..., x_{n-1}\n",
"X = [a + j*h for j ∈ 0:n] \n",
"\n",
"φ(i,x) = max(0, 1-abs( (x-X[i+1])/h ) )\n",
"\n",
"P = plot( x -> φ(1,x), a, b; \n",
" ylims=[-.15,1], label=L\"\\phi_1(x)\", lw=2)\n",
"plot!( x -> φ(2,x), a, b; label=L\"\\phi_2(x)\", lw=2)\n",
"scatter!( X, zeros(n+1), label=\"grid\", color=:black)\n",
"for i = 0:n\n",
" annotate!( X[i+1], -.05, text(L\"x_%$i\") )\n",
"end\n",
"\n",
"P"
]
},
{
"attachments": {
"FEM-2d.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"id": "602c5016",
"metadata": {},
"source": [
"::: {#rem-}\n",
"\n",
"The two dimensional analog of these hat functions look like this:\n",
"\n",
"\n",
"\n",
"One often uses triangles (as in this case) but you can also use rectangles, hexagons, ...\n",
"\n",
":::"
]
},
{
"cell_type": "markdown",
"id": "673fe12a",
"metadata": {},
"source": [
"One can write any piecewise linear function on the mesh with zero boundary conditions as a linear combination of $\\phi_j$ for $j=1,\\dots,n-1$. Moreover, the piecewise linear interpolation of some function $f$ on the grid can be written \n",
"\n",
"\\begin{align}\n",
" If(x) &= \\sum_{j=0}^n f(x_j) \\phi_j(x)\n",
"\\end{align}\n",
"\n",
"We show this in the following plot:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "ad9f83df",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
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"text/html": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(x) = x^2 * sin(2π * x)\n",
"If(x) = sum( f(X[i+1]) * φ(i,x) for i ∈ 0:n )\n",
"\n",
"plot(f, 0,1, label=L\"f\")\n",
"plot!(If, label=L\"If\")\n",
"scatter!( X, f.(X), label=L\"( x_j, f(x_j) )\", color=:black )"
]
},
{
"cell_type": "markdown",
"id": "6c2d3c8d",
"metadata": {},
"source": [
"The \"finite elements\" in this case refer to the intervals $I_j = [x_j,x_{j-1}]$. In 2d, one often uses triangles, ....\n",
"\n",
"**Step 2.** Recall that we want to build the matrices $K, M$ and the vector $F$:\n",
"\n",
"\\begin{align}\n",
" K_{ij} &= \\int_a^b \\alpha(x) \\phi_i'(x) \\phi_j'(x) \\mathrm{d}x \\nonumber\\\\\n",
" M_{ij} &= \\int_a^b \\beta(x) \\phi_i(x) \\phi_j(x) \\mathrm{d}x \\nonumber\\\\\n",
" F_i &= \\int_a^b f(x) \\phi_i(x) \\mathrm{d}x \n",
"\\end{align}\n",
"\n",
"(and then solve $(K+M)u = F$ to obtain a (piecewise linear) approximation to the exact solution to the continuous problem).\n",
"\n",
"Unless $\\alpha, \\beta, f$ are \"simple\", in practice one implements various quadrature schemes (Chapter 4 of Math 5485) to approximate these integrals. Perhaps the easiest thing you can do is, on each interval $I_k = [x_{k-1}, x_k]$, replace the function $\\alpha, \\beta, f$ with a constant and evaluate the resulting integral exactly:\n",
"\n",
"\\begin{align}\n",
" K_{ij} &\\approx \\sum_{k=1}^n \\frac{\\alpha(x_{k-1})+\\alpha(x_k)}{2} \\int_{I_k} \\phi_i'(x) \\phi_j'(x) \\mathrm{d}x \\nonumber\\\\\n",
" %\n",
" M_{ij} &\\approx \\sum_{k=1}^n \\frac{\\beta(x_{k-1})+\\beta(x_k)}{2} \\int_{I_k} \\phi_i(x) \\phi_j(x) \\mathrm{d}x \\nonumber\\\\\n",
" %\n",
" F_i &\\approx \\sum_{k=1}^n \\frac{f(x_{k-1})+f(x_k)}{2} \\int_{I_k} \\phi_i(x) \\mathrm{d}x\n",
"\\end{align}\n",
"\n",
"::: {#exr-K}\n",
"\n",
"Show that \n",
"\n",
"\\begin{align}\n",
" \\int_{I_k} \\phi_i'(x) \\phi_j'(x) \\mathrm{d}x\n",
" %\n",
" &= \n",
" \\frac1h\n",
" \\begin{cases}\n",
" 1 & \\text{if } i = j \\in \\{k, k-1\\} \\\\\n",
" -1 & \\text{if } \\{i,j\\} = \\{k,k-1\\}\\\\\n",
" 0 & \\text{otherwise}\n",
" \\end{cases} \n",
"\\end{align}\n",
"\n",
"In particular, if $\\alpha(x) = \\rm const.$, then \n",
"\n",
"\\begin{align}\n",
" K_{ij} &= \\frac1h\n",
" \\begin{cases}\n",
" 2 & \\text{if } i = j \\nonumber\\\\\n",
" -1 & \\text{if } |i-j| \\nonumber\\\\\n",
" 0 & \\text{otherwise}.\n",
" \\end{cases} \n",
"\\end{align}\n",
"\n",
"What do you notice about this matrix?\n",
"\n",
":::\n",
"\n",
"::: {#exr-M}\n",
"\n",
"Show that \n",
"\n",
"\\begin{align}\n",
" \\int_{I_k} \\phi_i(x) \\phi_j(x) \\mathrm{d}x\n",
" %\n",
" &= \n",
" \\frac{h}{3}\n",
" \\begin{cases}\n",
" 1 & \\text{if } i=j \\in \\{k,k-1\\}\\\\\n",
" \\frac12 & \\text{if } \\{i,j\\} = \\{k,k-1\\}\\\\\n",
" 0 &\\text{otherwise}.\n",
" \\end{cases} \n",
"\\end{align}\n",
"\n",
"Show that \n",
"\n",
"\\begin{align}\n",
" \\int_{I_k} \\phi_i(x) \\mathrm{d}x = \n",
" \\frac{h}{2}\\begin{cases}\n",
" 1 &\\text{if } i \\in \\{k,k-1\\} \\\\\n",
" 0 &\\text{otherwise}\n",
" \\end{cases}\n",
"\\end{align}\n",
"\n",
":::"
]
},
{
"cell_type": "markdown",
"id": "1db47da4",
"metadata": {},
"source": [
"**Step 3.** Solve the linear system of equations (we use the built in function ```u = A \\ F```) - see Chapter 2!"
]
},
{
"cell_type": "markdown",
"id": "d090cb4b",
"metadata": {},
"source": [
"We implement this here: "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "fbf57a22",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"fem"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
" fem(n, α, β, f; a=0, b=1)\n",
"\n",
"Approximate the solution to \n",
" -(α u′)′ + β u = f on (a,b)\n",
" u(a) = 0, u(b) = 0\n",
"using finite element method with hat functions\n",
"\"\"\"\n",
"function fem(n, α, β, f; a=0, b=1)\n",
" h = (b-a) / n\n",
" x = a .+ h .* (0:n)\n",
"\n",
" α_av = (α.(x[1:n])+α.(x[2:n+1]))/2\n",
" β_av = (β.(x[1:n])+β.(x[2:n+1]))/2\n",
" f_av = (f.(x[1:n])+f.(x[2:n+1]))/2\n",
"\n",
" K_d = [ (α_av[i]+α_av[i+1])/h for i ∈ 1:n-1 ] \n",
" K_dl = [ -α_av[i+1]/h for i ∈ 1:n-2 ] \n",
" K = SymTridiagonal(K_d, K_dl)\n",
"\n",
" M_d = [ h/3 *(β_av[i] + β_av[i+1]) for i ∈ 1:n-1 ]\n",
" M_dl = [ h/6 *β_av[i+1] for i ∈ 1:n-2 ]\n",
" M = SymTridiagonal(M_d, M_dl)\n",
" \n",
" F = [ (h/2) * ( f_av[i] + f_av[i+1] ) for i = 1:n-1 ]\n",
" \n",
" u = (K+M) \\ F\n",
" u = [0; u; 0] \n",
" return x, u\n",
"end"
]
},
{
"cell_type": "markdown",
"id": "becd3ca8",
"metadata": {},
"source": [
"::: {#exm-}\n",
"# @FNC Example 10.6.2\n",
"\n",
"Let's apply this to the following problem \n",
"\n",
"\\begin{align}\n",
" &-(x^2 u')' + 4u = \\sin \\pi x && \\text{on }(0,1) \\nonumber\\\\\n",
" %\n",
" &u(0) = u(1) = 0\n",
"\\end{align}\n",
"\n",
"* Write this in the form $-u'' + p u' + q = f$,\n",
"* Let's see how our finite element method compares to the finite difference method we had last time:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "51924120",
"metadata": {},
"outputs": [
{
"data": {
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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p(x) = -2/x\n",
"q(x) = 4/x^2\n",
"g(x) = sin(π*x)/x^2 \n",
"\n",
"α(x) = x^2\n",
"β(x) = 4\n",
"f(x) = sin(π*x)\n",
"\n",
"x, u = fem(25, α, β, f)\n",
"plot(x, u; \n",
" label=\"finite element method\", markersize=2, m=2)\n",
"\n",
"x2, u2 = fdm(25, p, q, g)\n",
"P1 = scatter!(x2, u2; \n",
" label=\"finite difference method\", markersize=2)"
]
},
{
"cell_type": "markdown",
"id": "e15f492a",
"metadata": {},
"source": [
"Here is the error curve for both:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "fe4891a8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
""
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# we measure the error on the grid egrid:\n",
"egrid = range(0,1,500)\n",
"\n",
"# compute a reference solution to compute the error against\n",
"x, u = fem(2^15, α, β, f)\n",
"u_e = linear_interpolation(x, u)\n",
"\n",
"nn = [2^j for j∈2:12]\n",
"err_fem = zeros(length(nn))\n",
"err_fdm = zeros(length(nn))\n",
"\n",
"for (i,n) ∈ enumerate(nn)\n",
" x, u = fem(n, α, β, f)\n",
" uf = linear_interpolation(x, u)\n",
" err_fem[i] = abs.( maximum(uf.(egrid) - u_e.(egrid)) ) \n",
"\n",
" x, u = fdm(n, p, q, g)\n",
" uf = linear_interpolation(x, u)\n",
" err_fdm[i] = abs.( maximum(uf.(egrid) - u_e.(egrid)) ) \n",
"end\n",
"\n",
"plot( nn, err_fem;\n",
" xaxis=:log,yaxis=:log, m=2, xlabel=L\"n\", ylabel=\"error\",\n",
" label=\"FEM\" )\n",
"plot!( nn, err_fdm;\n",
" label=\"FDM\", m=2 )\n",
"plot!( nn[3:end], nn[3:end].^(-2), linestyle=:dash, label=L\"O(h^2)\")"
]
},
{
"cell_type": "markdown",
"id": "314056d9",
"metadata": {},
"source": [
":::"
]
},
{
"cell_type": "markdown",
"id": "83727fa4",
"metadata": {},
"source": [
"::: {#exr-}\n",
"\n",
"Now suppose we want to solve the BVP with non-zero boundary conditions:\n",
"\n",
"\\begin{align}\n",
" &-(\\alpha u')' + \\beta u = f \\qquad \\text{on } (a,b) \\nonumber\\\\\n",
" &u(a) = A, \\qquad u(b) = B.\n",
"\\end{align}\n",
"\n",
"Show that \n",
"\n",
"\\begin{align}\n",
" u(x) &= v(x) + \\theta x + \\varphi\n",
"\\end{align}\n",
"\n",
"with $\\theta := \\frac{B-A}{b-a}$ and $\\varphi := \\frac{Ab - Ba}{b-a}$ and $v$ solves the problem\n",
"\n",
"\\begin{align}\n",
" &-(\\alpha v')' + \\beta v = f + \\theta \\alpha' - \\beta( \\theta x + \\varphi ) \\qquad \\text{on } (a,b) \\nonumber\\\\\n",
" &v(a) = 0, \\qquad v(b) = 0.\n",
"\\end{align}\n",
"\n",
"How can you use this and the function ```fem()``` to approximate the solution to the BVP with non-zero boundary conditions?"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "34244da2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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"\n",
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""
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a, b, A, B = 0, 1, 0, 1/2 \n",
"α(x) = x^2\n",
"α′(x) = 2x\n",
"β(x) = 4\n",
"f(x) = sin(π*x)\n",
"\n",
"θ = (B-A)/(b-a)\n",
"ϕ = (A*b - B*a)/(b-a)\n",
"\n",
"# transformed RHS \n",
"f_shift(x) = f(x) + θ*α′(x) - β(x)*(θ*x + ϕ)\n",
"\n",
"x, v = fem(5, α, β, f_shift; a, b)\n",
"u = v + θ*x .+ ϕ\n",
"P = plot(x, u; \n",
" label=\"finite element method\", markersize=2, m=2)\n",
"\n",
"x2, u2 = fdm(5, p, q, g; a, b, A, B )\n",
"plot!(x2, u2; \n",
" label=\"finite difference method\", markersize=2, m=2)"
]
},
{
"cell_type": "markdown",
"id": "d18159b0",
"metadata": {},
"source": [
":::"
]
},
{
"cell_type": "markdown",
"id": "b1d5ab0c",
"metadata": {},
"source": [
":::{.callout-tip}\n",
"# TO-DO\n",
"\n",
"* Today: @FNC [Galerkin method](https://fncbook.com/galerkin/)\n",
"* Take a look at the suggestions for [Presentations/Posters/Papers](/Presentations.html) and sign up to present, \n",
"* Read through the proofs/exercises from this lecture and Monday, \n",
"* (Sign-up to office hours if you would like)\n",
"\n",
"Previous reading:\n",
"\n",
"* Chapter 1 reading:\n",
" * @Burden sections 5.1 - 5.6, \n",
" * @FNC [zero stability](https://fncbook.com/zerostability/) \n",
"* Chapter 2 reading:\n",
" * Recap matrices: sections 7.1 - 7.2 of @Burden \n",
" * Jacobi & Gauss-Seidel: section 7.3 @Burden \n",
" * CG: section 7.6 @Burden\n",
"* Chapter 3 reading: \n",
" * Sections 11.1 - 11.2 of @Burden: shooting methods\n",
"\n",
":::"
]
}
],
"metadata": {
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"language": "julia",
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