Hello Laura,
IIRC, the exact solution class is to enable comparisons
of a numerical solution with an analytic solution. Since you are seeking to
compare a coarse and fine numerical solution, I think the
UniformRefinementEstimator might be the right functionality to use.
Adaptivity example 3 (libmesh/examples/adaptivity/adaptivity_ex3) might be
a good place to start. It provides examples of the use of both
ExactErrorEstimator and UniformRefinementEstimator.
Thanks.
On Wed, Jun 21, 2017 at 2:48 PM, Laura Scarabosio <scara...@ma.tum.de>
wrote:
> Hi everybody,
>
> I would like to perform a convergence study computing the difference in L2
> and H1 norm between the solution on a coarser grid and another one on a
> finer grid, obtained using uniformly_refine().
>
> To do this, I saved the two meshes and solutions in .xdr. Then I took the
> meshdiff.C implementation in the src/apps folder, and made a simplification
> of it. The code uses the ExactSolution class and looks like this:
>
> int main(int argc, char ** argv)
> {
> LibMeshInit init(argc, argv);
>
> Mesh coarse_mesh(init.comm(), dim), fine_mesh(init.comm(), dim);
> EquationSystems coarse_es(coarse_mesh), fine_es(fine_mesh);
>
> libMesh::out << "Usage: " << argv[0]
> << " coarsemesh coarsesolution finemesh finesolution
> [outputdiff]" << std::endl;
>
> if (argc < 5)
> libmesh_error();
>
> coarse_mesh.read(argv[1]);
> libMesh::out << "Loaded coarse mesh " << argv[1] << std::endl;
> coarse_es.read(argv[2]);
> libMesh::out << "Loaded coarse solution " << argv[2] << std::endl;
> fine_mesh.read(argv[3]);
> libMesh::out << "Loaded fine mesh " << argv[3] << std::endl;
> fine_es.read(argv[4]);
> libMesh::out << "Loaded fine solution " << argv[4] << std::endl;
>
> ExactSolution exact_sol(coarse_es);
> exact_sol.attach_reference_solution(&fine_es);
>
> exact_sol.compute_error("S0_Tum", "v0_tum");
>
> const System & coarse_sys = coarse_es.get_system("S0_Tum");
> const System & fine_sys = fine_es.get_system("S0_Tum");
>
>
> libMesh::out << "Errors in system " << "S0_Tum" << ", variable " <<
> "v0_tum" << ":" << std::endl;
> libMesh::out << "L2 error: " << exact_sol.l2_error("S0_Tum", "v0_tum")
> << ", coarse norm: " <<
> coarse_sys.calculate_norm(*coarse_sys.solution,
> 0, L2)
> << ", fine norm: " <<
> fine_sys.calculate_norm(*fine_sys.solution,
> 0, L2) << std::endl;
> libMesh::out << "H1 error: " << exact_sol.h1_error("S0_Tum", "v0_tum")
> << ", coarse norm: " <<
> coarse_sys.calculate_norm(*coarse_sys.solution,
> 0, H1)
> << ", fine norm: " <<
> fine_sys.calculate_norm(*fine_sys.solution,
> 0, H1) << std::endl;
>
>
> return 0;
> }
>
> Then I launch it, for example, with
>
> ./main cvg_study/mesh_0refs_b.xdr cvg_study/solution_0refs_b.xdr
> cvg_study/mesh_1refs_b.xdr cvg_study/solution_1refs_b.xdr
>
> However, when the L2 and H1 errors are printed on screen, they are the
> very same as the norm of the solution on the fine mesh. It seems like the
> solution on the coarse mesh gets not subtracted. I tried printing on screen
> the solution from the system on the coarse grid, and it looked ok
> (nonzero), and looking at the previous discussion
> https://sourceforge.net/p/libmesh/mailman/message/25861781/, it seems I
> am in the right direction, so I cannot really understand what is going
> wrong. Could anyone help me understanding what is the problem with my code?
>
> Thank you,
> Laura.
>
> ------------------------------------------------------------
> ------------------
> Check out the vibrant tech community on one of the world's most
> engaging tech sites, Slashdot.org! http://sdm.link/slashdot
> _______________________________________________
> Libmesh-users mailing list
> Libmesh-users@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/libmesh-users
>
--
Vikram Garg
Postdoctoral Associate
The University of Texas at Austin
http://vikramvgarg.wordpress.com/
http://www.runforindia.org/runners/vikramg
------------------------------------------------------------------------------
Check out the vibrant tech community on one of the world's most
engaging tech sites, Slashdot.org! http://sdm.link/slashdot
_______________________________________________
Libmesh-users mailing list
Libmesh-users@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/libmesh-users
