ex6: I tried with exacmple C

Sheet6/Ex6C.m

@@ -30,9 +30,16 @@ for it = 1:nIter
             %Jump in convection-diffusion flux
             Jl = -ul + p*u(j);
             Jr = -ur + p*u(j);
+            % GH
+            % JL = (u(j)-u(j-1))/(x(j)-x(j-1))*(x(j)-x(j-1));
+            % JR = (u(j+1)-u(j))/(x(j+1)-x(j))*(x(j+1)-x(j));
+            % HG
             eta(j) = abs(Jr - Jl);
+            %GH eta(j) = abs(Jr - Jl)*sqrt((x(j)-x(j-1))*(x(j+1)-x(j)));
+            %GH eta(j) = abs(Jr - Jl)*sqrt(max((x(j)-x(j-1)),(x(j+1)-x(j))));
         end
         x = r_adapt(x, eta);
+        %
     end
 end
 
@@ -41,3 +48,8 @@ plot(x,u,'-o','LineWidth',1.5)
 xlabel('x'), ylabel('u')
 title(['Ex6C, r-adaptivity, Péclet p = ',num2str(p)])
 grid on
+% GH
+hold on
+fplot(@(x) (exp(p*x)-1)/(exp(p)-1),[0,1])
+% Finalize the plot with the exact solution for comparison
+legend('Numerical Solution', 'Exact Solution', 'Location', 'Best');

Sheet6/gh_response.txt

@@ -13,4 +13,4 @@ B:
 C:
 * r-adaptivity
   looks suspicious, but similar to Mandl
-
+  cumsum in r_adapt() not correct, but exact cumsum results in wrong solution behavior

Sheet6/r_adapt.m

@@ -3,7 +3,8 @@ N = length(x);
 w = abs(eta_elem) + 1e-10; %error based monitor function
 s = zeros(N,1); 
 for i = 2:N
-    s(i) = s(i-1) + w(i-1); %cumulative sum
+    s(i) = s(i-1) + w(i-1); %cumulative sum  % LP
+    % s(i) = s(i-1) + w(i); %cumulative sum  % GH
 end
 s = s / s(end);   % normalize to [0,1]
 s_new = linspace(0,1,N)';