On p-robust saturation for hp-AFEM

For the Poisson problem in two dimensions, we consider the standard adaptive finiteelement loop solve, estimate, mark, refine, with estimate being implemented using thep-robust equilibrated flux estimator, and, mark being Dörfler marking. As a refinementstrategyweemployp-refinement.Weinvestigatethequestionbywhichamountthelocalpolynomial degree on any marked patch has to be incremented in order to achieve ap-independent error reduction. We show that the analysis can be transferred from thepatchestoareferencetriangle,andthereinweprovideclear-cutcomputationalevidencethat any increment proportional to the polynomial degree (for any fixed proportionalityconstant)yieldsthedesiredreduction.Theresultingadaptivemethodcanbeturnedintoaninstanceoptimalhp-adaptivemethodbytheadditionofacoarseningroutine.