Adaptive Crouzeix-Raviart Boundary Element Method

2013/12/02 by Heuer, Norbert, Karkulik, Michael
#65N30 #65N38 #65N50 #65R20 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1312.0484

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 h-h/2 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.

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