Mortar Boundary Elements

TL;DR

This paper introduces a mortar boundary element method for 3D hypersingular boundary integral equations, demonstrating almost optimal convergence even with non-conforming sub-domain decompositions and quasi-uniform meshes, supported by numerical validation.

Contribution

It develops a novel mortar boundary element scheme for hypersingular equations with proven convergence properties and flexible mesh requirements.

Findings

Almost quasi-optimal convergence in broken Sobolev norms

Compatibility with non-conforming sub-domain decompositions

Numerical results confirm theoretical predictions

Abstract

We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. Numerical results confirm the theory.