On the coupling of DPG and BEM

TL;DR

This paper introduces new strategies for coupling the discontinuous Petrov-Galerkin method with boundary element methods, enabling local computation of optimal test functions for boundary integral equations, validated through numerical experiments.

Contribution

It develops and analyzes novel coupling strategies that allow local computation of optimal test functions in boundary element methods, improving efficiency and accuracy.

Findings

Optimal test functions can be computed locally despite boundary integral equations.

The proposed methods are effective for standard transmission problems.

Numerical experiments confirm the theoretical advantages.

Abstract

We develop and analyze strategies to couple the discontinuous Petrov-Galerkin method with optimal test functions to (i) least-squares boundary elements and (ii) various variants of standard Galerkin boundary elements. Essential feature of our methods is that, despite the use of boundary integral equations, optimal test functions have to be computed only locally. We apply our findings to a standard transmission problem in full space and present numerical experiments to validate our theory.