From 4a6a9a2f24e01f92d26d877706896c09cec30a39 Mon Sep 17 00:00:00 2001 From: "lisa.pizzo" Date: Mon, 24 Nov 2025 10:13:54 +0100 Subject: [PATCH] Delete Sheet4/Ex1.m --- Sheet4/Ex1.m | 50 -------------------------------------------------- 1 file changed, 50 deletions(-) delete mode 100644 Sheet4/Ex1.m diff --git a/Sheet4/Ex1.m b/Sheet4/Ex1.m deleted file mode 100644 index 7745237..0000000 --- a/Sheet4/Ex1.m +++ /dev/null @@ -1,50 +0,0 @@ -%% FEM vs analytical solution for -u'' + a*u = f, mixed BC -clear; clc; -%% Parameters -n = 10; % number of elements -a = 2; % reaction term -alpha = 5; % Robin BC -gB = 1; % Robin BC value -f = 3; % constant RHS -h = 1/n; -x = linspace(0,1,n+1); - -%% Assemble FEM matrices -A = zeros(n+1,n+1); -F = zeros(n+1,1); - -% Linear shape functions, 1D FEM -K_diff = (1/h)*[1,-1;-1,1]; -K_reac = a*(h/6)*[2,1;1,2]; - -for e=1:n - nodes = [e, e+1]; - A(nodes,nodes) = A(nodes,nodes) + K_diff + K_reac; - F(nodes) = F(nodes) + f*(h/2)*[1;1]; % f*v integral approx -end - -% Dirichlet BC u(0)=0 -A(1,:) = 0; A(:,1) = 0; A(1,1) = 1; -F(1) = 0; - -% Robin BC at x=1 -A(end,end) = A(end,end) + alpha; -F(end) = F(end) + alpha*gB; - -%% Solve FEM -u_fem = A\F; - -%% Analytical solution -syms C -C1 = (alpha*gB - (f/a)*alpha*(1 - exp(-sqrt(a))) - (f/sqrt(a))*exp(-sqrt(a))) ... - / (alpha*sinh(sqrt(a)) + sqrt(a)*cosh(sqrt(a))); -u_exact = @(x) C1*sinh(sqrt(a)*x) + (f/a)*(1 - exp(-sqrt(a)*x)); -u_an = u_exact(x); - -%% Plot -plot(x,u_fem,'o-','LineWidth',2); hold on; -plot(x,u_an,'r--','LineWidth',2); -legend('FEM','Analytical'); -xlabel('x'); ylabel('u(x)'); -title('FEM vs Analytical solution'); -grid on;