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Sheet6/Ex6C.m

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+clear; clc; close all;
+p = 70;
+%p=-70;
+lambda = @(x) 1; %constant diffusion
+f = @(x) 0; %homogeneous RHS
+
+N = 30;     % Initial mesh (uniform)
+x = linspace(0,1,N)';
+
+nIter = 8;
+
+for it = 1:nIter
+    [K,F] = assemble_1D(x,lambda,f); %assemble 
+    for i = 1:length(x)-1 %convection term added manually
+        h = x(i+1) - x(i);
+        Ke_conv = p/2 * [-1 1; -1 1]; 
+        K(i:i+1,i:i+1) = K(i:i+1,i:i+1) + Ke_conv;
+    end
+    K(1,:) = 0; K(1,1) = 1; F(1) = 0; % Dirichlet BC at x=0
+    K(end,:) = 0; K(end,end) = 1; F(end) = 1; % Dirichlet BC at x=1
+
+    u = K\F;
+
+    if it < nIter
+        Nn = length(x); %initialize indicator
+        eta = zeros(Nn,1);
+        for j = 2:Nn-1 %interior nodes only
+            ul = (u(j)-u(j-1))/(x(j)-x(j-1)); %left derivative
+            ur = (u(j+1)-u(j))/(x(j+1)-x(j)); %right derivative
+            %Jump in convection-diffusion flux
+            Jl = -ul + p*u(j);
+            Jr = -ur + p*u(j);
+            eta(j) = abs(Jr - Jl);
+        end
+        x = r_adapt(x, eta);
+    end
+end
+
+figure
+plot(x,u,'-o','LineWidth',1.5)
+xlabel('x'), ylabel('u')
+title(['Ex6C, r-adaptivity, Péclet p = ',num2str(p)])
+grid on