ZZ-type aposteriori error estimators for adaptive boundary element methods on a curve

TL;DR

This paper introduces and analyzes ZZ-type a posteriori error estimators for adaptive boundary element methods, demonstrating their convergence for weakly-singular and hyper-singular integral equations.

Contribution

It extends ZZ-error estimators from FEM to BEM, providing theoretical analysis and convergence results for adaptive algorithms.

Findings

Proposed ZZ-type estimators for BEM

Proved convergence of adaptive mesh refinement

Applicable to weakly-singular and hyper-singular equations

Abstract

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly-singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms.