Hi, all. I have asked whether numerical errors also behave ~O(h^p) , even though governing equation is non-linear and thus, a solver includes iterative method. I recall that Dr. Bangerth replied me it is "yes" if we imply small enough tolerance on iteration tolerance. I am trying to confirm this testing the code with Picard Iteration, ( Dr. Bangerth's video lecture from 31.5~31.7)
To bring the governing equation again <https://lh3.googleusercontent.com/-TYzXkQCHcTA/WAksZOt6tjI/AAAAAAAAA7E/kX0e1wXWcfMcKc-dDYeq2rOOmXi-YtHjwCLcB/s1600/Screen%2BShot%2B2016-10-20%2Bat%2B3.42.54%2BPM.png> Since I want to test the code really has correct h-p convergence, I used the method of manufactured solution. To be specific, I assumed solution as " u(x,y)= <https://lh3.googleusercontent.com/-dBW9xWRIpWE/WBkKfMK0QPI/AAAAAAAAA7c/SURwfidSLLAUL0ZrA94wn_sheykuZTDyACLcB/s1600/Screen%2BShot%2B2016-11-01%2Bat%2B4.34.36%2BPM.png> " and this gives me a right hand side function, f , f= <https://lh3.googleusercontent.com/-YdYt94kXCtc/WBkK3hcHHTI/AAAAAAAAA7g/iLbRiSE6hJk9Vvdpkc9uhQFhumJOuzpCQCLcB/s1600/Screen%2BShot%2B2016-11-01%2Bat%2B4.36.10%2BPM.png>where z=x^2+y^2 After that I imposed boundary condition as exact with u(x,y) = <https://lh3.googleusercontent.com/-dBW9xWRIpWE/WBkKfMK0QPI/AAAAAAAAA7c/SURwfidSLLAUL0ZrA94wn_sheykuZTDyACLcB/s1600/Screen%2BShot%2B2016-11-01%2Bat%2B4.34.36%2BPM.png> =g Lastly, I compared my numerical solution with manufactured exact solution using Vectortools::integrate_difference. l2norm template <int dim> void msurface<dim>::evaluate_error() { Vector<float> difference_per_cell (triangulation.n_active_cells()); VectorTools::integrate_difference (dof_handler,solution,Solution<dim>(), difference_per_cell,QGauss<dim>(degree+2),VectorTools::L2_norm); const double L2_error = difference_per_cell.l2_norm(); std::cout << " L2_error : " << L2_error << std::endl; error=L2_error; } However, I the error graph I get was as follow... <https://lh3.googleusercontent.com/-YGzF49KtLZ8/WBkL1TaMVfI/AAAAAAAAA7s/yYA3RR2pPP0gTEbjRPkqaviDfjZJXDP7gCLcB/s1600/case1.jpg> I think that I didn't make any mistake on my code lines because at least my numerical solution is converging for the case p=1. but I couldn't get such convergence for the case p=2, and 3. I have tried to change tolerance number in iterative scheme, but it didn't work. Are there other things that I failed to consider? Or did I make wrong way to test the code? Always thank you for all smart guys here!! Jaekwang Kim -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
