Analysis of a non-symmetric coupling of Interior Penalty DG and BEM

TL;DR

This paper investigates a non-symmetric coupling of interior penalty discontinuous Galerkin and boundary element methods, establishing discrete coercivity, unique solvability, and quasi-optimal convergence in 2D and 3D, supported by numerical evidence.

Contribution

It provides a novel analysis of a non-symmetric coupling method, proving coercivity and convergence using localized variational techniques and fractional Sobolev space analysis.

Findings

Proves discrete coercivity and unique solvability of the coupled method.

Establishes quasi-optimal convergence rates.

Numerical evidence supports theoretical results.

Abstract

We analyze a non-symmetric coupling of interior penalty discontinuous Galerkin and boundary element methods in two and three dimensions. Main results are discrete coercivity of the method, and thus unique solvability, and quasi-optimal convergence. The proof of coercivity is based on a localized variant of the variational technique from [F.-J. Sayas, The validity of Johnson-N\'edel\'ec's BEM-FEM coupling on polygonal interfaces, {\em SIAM J. Numer. Anal.}, 47(5):3451--3463, 2009]. This localization gives rise to terms which are carefully analyzed in fractional order Sobolev spaces, and by using scaling arguments for rigid transformations. Numerical evidence of the proven convergence properties has been published previously.