English

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 pp-robust equilibrated flux estimator, and MARK being D\"orfler marking. As a refinement strategy we employ pp-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 pp-independent error reduction. The resulting adaptive method can be turned into an instance optimal hphp-adaptive method by the addition of a coarsening routine.

Keywords

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}
}
R2 v1 2026-06-22T16:50:36.331Z