Uploading ex6

Sheet_6/adapt_r.m

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+% r-adaptivity
+% for a given mesh and solution we generate a new adapted mesh by moving
+% the existing nodes within the mesh; they get moved to a position in order
+% to equally distribute the error over the intervall
+% we use the De Boor's algorithm (Huang, Russell; Adaptive Moving Mesh
+% Methods; $ 2.2.1)
+
+function mesh = adapt_r(nodes,u,lambda)
+    n_nodes = length(nodes);
+    flux_jumps = abs(jumps_flux(nodes,u,lambda));
+    p = 1/2*(flux_jumps(1:end-1) + flux_jumps(2:end));  % has values for each element
+    h_vec = nodes(2:end) - nodes(1:end-1);
+    P = cumsum(h_vec'.*p);
+    P = [0;P];
+    xi = linspace(0,1,n_nodes);
+    mesh = nodes;
+    for j=2:n_nodes-1
+        idx_k = find(xi(j)*P(end) <= P, 1, 'first');
+        if idx_k > 1
+            x_j = nodes(idx_k-1) + xi(j)*(P(end)-P(idx_k -1))/p(idx_k -1);
+            mesh(j) = x_j;
+        end
+    end
+end