Adaptive Crouzeix-Raviart Boundary Element Method
Numerical Analysis
2013-12-03 v1
Abstract
For the non-conforming Crouzeix-Raviart boundary elements from [Heuer, Sayas: Crouzeix-Raviart boundary elements, Numer. Math. 112, 2009], we develop and analyze a posteriori error estimators based on the methodology. We discuss the optimal rate of convergence for uniform mesh refinement, and present a numerical experiment with singular data where our adaptive algorithm recovers the optimal rate while uniform mesh refinement is sub-optimal. We also discuss the case of reduced regularity by standard geometric singularities to conjecture that, in this situation, non-uniformly refined meshes are not superior to quasi-uniform meshes for Crouzeix-Raviart boundary elements.
Cite
@article{arxiv.1312.0484,
title = {Adaptive Crouzeix-Raviart Boundary Element Method},
author = {Norbert Heuer and Michael Karkulik},
journal= {arXiv preprint arXiv:1312.0484},
year = {2013}
}