Inverse estimates for elliptic boundary integral operators and their application to the adaptive coupling of FEM and BEM

TL;DR

This paper establishes inverse estimates for classical boundary integral operators related to Laplace's equation and applies these results to prove convergence of an adaptive FEM-BEM coupling algorithm driven by a residual error estimator.

Contribution

The paper introduces inverse estimates for boundary integral operators and demonstrates their use in proving convergence of an adaptive FEM-BEM coupling method.

Findings

Proved inverse estimates for boundary integral operators.

Established convergence of an adaptive FEM-BEM algorithm.

Validated the effectiveness of a residual error estimator.

Abstract

We prove inverse-type estimates for the four classical boundary integral operators associated with the Laplace operator. These estimates are used to show convergence of an h-adaptive algorithm for the coupling of a finite element method with a boundary element method which is driven by a weighted residual error estimator.