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

TL;DR

This paper develops and analyzes an a posteriori error estimator for a non-conforming boundary element method solving hypersingular boundary integral equations, demonstrating its effectiveness through theoretical analysis and numerical experiments.

Contribution

It introduces a new a posteriori error estimator for a non-conforming boundary element method using Nitsche's technique, with proven reliability and efficiency.

Findings

The estimator is quasi-reliable and efficient under a saturation assumption.

Numerical experiments confirm the theoretical error bounds.

Adaptive mesh refinement improves solution accuracy.

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.