Dear Markus, Wolfgang, Am Donnerstag, den 21.04.2011, 21:49 -0500 schrieb Wolfgang Bangerth: > > 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?
I had a setting in mind, where the square K is replaced by a ball B around some point (x,y). Taking the normal derivative of a rotationally symmetric function on the boundary of B and integrating these values gives a rotationally symmetric function in (x,y) altogether (keeping the radius of the ball fixed). > > 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. Of course (exact) rotational symmetry is lost in this setting, but I expected to get meshes which still "look" rotationally symmetric. But in my example, this is only the case for the first refinement steps, after some more steps the refined mesh roughly looks like a cross. Is there a way to damp this behavior? > > 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. > Thanks a lot for this interesting example. But what is the conclusion concerning my original question, obtaining good solutions with a minimal number of mesh points? Maybe I should weight the Kelly error depending on angle? Or are there better ideas? Thank you very much, Jochen > Best > W. > > ------------------------------------------------------------------------- > Wolfgang Bangerth email: [email protected] > www: http://www.math.tamu.edu/~bangerth/ -*-- _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
