Adaptive Crouzeix–Raviart boundary element method∗
Revised: 7 November 2014
For the nonconforming Crouzeix–Raviart boundary elements from [N. Heuer and F.-J. Sayas, Numer. Math. 112 (2009) 381–401], 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.
Mathematics Subject Classification: 65N30 / 65N38 / 65N50 / 65R20
Key words: Boundary element method / adaptive algorithm / nonconforming method / a posteriori error estimation
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