Discontinuous Galerkin hp-BEM with quasi-uniform meshes

TL;DR

This paper introduces and analyzes a discontinuous hp-version boundary element method with quasi-uniform meshes for hypersingular integral equations on polyhedral surfaces, providing quasi-optimal error estimates and numerical validation.

Contribution

It presents a novel discontinuous hp-BEM formulation with theoretical error bounds and demonstrates its effectiveness through numerical experiments.

Findings

Quasi-optimal error estimates for the method.

Convergence orders are quasi-optimal for h-version and nearly so for p-version.

Numerical results confirm the theoretical predictions.

Abstract

We present and analyze a discontinuous variant of the hp-version of the boundary element Galerkin method with quasi-uniform meshes. The model problem is that of the hypersingular integral operator on an (open or closed) polyhedral surface. We prove a quasi-optimal error estimate and conclude convergence orders which are quasi-optimal for the h-version with arbitrary degree and almost quasi-optimal for the p-version. Numerical results underline the theory.