A posteriori error analysis for a boundary element method with non-conforming domain decomposition

2013/07/27 by Domínguez, Catalina, Heuer, Norbert
#65N38 #65N55 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1307.7310

Abstract

We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a non-conforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasi-reliability and efficiency of the error estimator in comparison with the error in a natural (non-conforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results.

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