Hello everyone,
I want to ask about a problem in the computation of error and in the
exportation of solution to ".vtk" file:
*First Problem :*
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.
--
*ZAIM Yassine *
*PhD Student in Applied Mathematics*
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