I want to ask about a problem in the computation of error and in the exportation of solution to ".vtk" file:
I have programmed a non-conforming element in two dimension which contains 6 degrees of freedom (4 in the vertices of rectangle + 2 second derivative with respect to each variable calculated in the center of rectangle). I apply this element to the planar elastic problem without pression. In the model "elastostatic.cc" of directory tests we find
if (data_fem_name.size() == 0) {
GMM_ASSERT1(pf_u->is_lagrange(), "You are using a non-lagrange FEM. "
<< "In that case you need to set "
<< "DATA_FEM_TYPE in the .param file");
mf_rhs.set_finite_element(pf_u); }...
So at the beginning I set the "DATA_FEM_TYPE =FEM_QK(2,1)" and FEM_TYPE = "my element" because my element is not of Lagrange type. I got an approximate solution which is not accurate when we look to the file "sol.vtk", but for the error I get an error with precision "e-7" and "e-6" for the L2 norm and H1 norm, respectively. The rate of convergence in this case for the both norms is "=2".
However when I use the same finite element "my element" for DATA_FEM_TYPE, FEM_TYPE and to apply the boundary conditions (just Dirichlet conditions in my case). I get an approximate solution more precise when I look to "Sol.vtk". The pourcentage of error is "Max value of error/max value of Exact solution = 5%" but in this case the error is too large and its precision is "e-2" for the norm L2 and "e-0" for the norm H1, but if I compute the order of convergence by these values of error, I got the optimal orde for H1 norm "=1" but I can't get it for the L2 norm "=0.33".
Second problem :
I have programmed a part to export 3 files which contain "Exact solution.vtk - Approximation Solution.vtk - Error.vtk" in the same mesh. When I show the vectors numerically and by computation also, I see that the max value and min value are different from the range of colorbar of Paraview. When I make rescale to the range of colorbar, I get two solutions verry different, which will be, I think juste a problem in the exportation.
I would add that I use a "gmm::ilutp_precond" preconditioner and "gmm::gmres or gmm::least_squares_cg or ..." solver because in my case the standard solver cannot exceed a certain number of subdivisions (Pivot too small).
I will be grateful, if some one have some suggestions.
Thank you in advance.