> I am studying a time dependent PDE on a square domain and want to > compare exactness of the solution to the number of dofs. I use the Kelly > estimator for local refinement. For testing the program, I use a > parameter setting allowing for a rotational symmetric analytic solution > at every time. Now I observe that the locally refined mesh is by far NOT > rotational symmetric, but rather symmetric along the coordinate axes, > although the (analytic) Kelly estimator is rotational symmetric for > rotational symmetric functions.
What would be the "analytic" Kelly estimator? The class computes the jump of the gradient of the numerical solution along the faces of cells. Not only will the numerical solution be rotationally symmetric, but the computation of edge integrals will also not be rotationally symmetric. I would therefore not be surprised at all if the resulting mesh is not symmetric. As an example for a case where something similar happens, take a look at the meshes generated by step-14: http://www.dealii.org/developer/doxygen/deal.II/step_14.html#Results The meshes result from the corner singularity or the singularity in the dual solution which -- at least close to the reentrant corner -- also has some sort of rotational symmetry. Yet, the meshes aren't rotationally symmetric. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
