Functional a posteriori error estimates for boundary element methods

TL;DR

This paper introduces a novel functional a posteriori error estimate for boundary element methods that provides guaranteed bounds independent of discretization, applicable to Galerkin BEM and collocation methods, validated through numerical experiments.

Contribution

It presents the first functional error estimate for BEM that offers guaranteed bounds and is independent of the discretization method.

Findings

Error estimates are independent of BEM discretization.

Guaranteed lower and upper bounds for errors are provided.

Numerical experiments confirm theoretical guarantees.

Abstract

Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.