Sheet 4 - solutions

Sheet_4/Ex_4_B.m

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+% Sheet 4 / Task B
+
+ne = 50;    % number of elements
+nodes = linspace(0,1,ne+1);
+
+K = zeros(ne+1,ne+1);   % global stiffness matrix
+f = zeros(ne+1,1);    % load vector
+
+lambda = @(x) (x<1/sqrt(2))*1 + (x>=1/sqrt(2))*10;
+
+for e = 1:ne
+    xleft = nodes(e);
+    xright = nodes(e+1);
+    Ke = ne^2*[integral(lambda,xleft,xright), -integral(lambda,xleft,xright);
+        -integral(lambda,xleft,xright), integral(lambda,xleft,xright)];
+    
+    K(e:e+1, e:e+1) = K(e:e+1, e:e+1) + Ke;
+end
+
+% disp(K)
+
+% adaption for dirichlet boundary
+K(1,1) = K(1,1)*(1 + 1e6);
+f(end) = K(end,end)*1e6;
+K(end,end) = K(end,end)*(1 + 1e6);
+
+u = K\f;
+
+plot(nodes,u)
+title('approximation of solution u');
+xlabel('x values');
+ylabel('u_h');