On p-Robust Saturation for hp-AFEM
Numerical Analysis
2016-11-15 v1
Abstract
We consider the standard adaptive finite element loop SOLVE, ESTIMATE, MARK, REFINE, with ESTIMATE being implemented using the -robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ -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 -independent error reduction. The resulting adaptive method can be turned into an instance optimal -adaptive method by the addition of a coarsening routine.
Cite
@article{arxiv.1611.04104,
title = {On p-Robust Saturation for hp-AFEM},
author = {Claudio Canuto and Ricardo H. Nochetto and Rob Stevenson and Marco Verani},
journal= {arXiv preprint arXiv:1611.04104},
year = {2016}
}