On p-robust saturation for hp-AFEM

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 Dörfler 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.