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

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.