On p-Robust Saturation for hp-AFEM
Thursday 17th November 2016
Canuto, C.; Nochetto, R. H.; Stevenson R.; Verani, M.
For the Poisson problem in two dimensions, we consider the standard adaptive finite element loop solve, estimate, mark, refine, with estimate being implemented using the $p$-robust equilibrated flux estimator, and, mark being Dorfler marking. As a refinement strategy we employ $p$-refinement. We investigate the question by which amount the local polynomial degree on any marked patch has to be increase in order to achieve a p-independent error reduction. The resulting adaptive method can be turned into an instance optimal $hp$-adaptive method by the addition of a coarsening routine.