> 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? > [...] > 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?
I think it is worth first investigating the underlying notion that the mesh you get is somehow "wrong". You assume that it should be rotationally symmetric, but this isn't completely clear to me. Consider, for example, approximating the function x^2 on the unit cell [0,1]^2 with bilinear functions. The rotate the function: try approximating the essentially same function (x*cos t)^2 + (y*sin t)^2 on the same cell. I bet that the error depends on the angle t. (It should be easy enough to compute the exact error in this case, for example if you use the interpolation as your approximation.) What I mean to say by this is that if you try to approximate a rotationally symmetric function on an axiparallel mesh, you need to expect that the error depends not only on the radius but also on the angle. As a consequence, you should expect that the optimal mesh size also depends on the angle. The Kelly estimator appears to give you one angularly dependent function (which may or may not be optimal). Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
