Analysis of a non-symmetric coupling of Interior Penalty DG and BEM
Provides theoretical justification for a numerical method coupling DG and BEM, which is incremental as it adapts existing variational techniques to a non-symmetric setting.
The paper proves discrete coercivity and quasi-optimal convergence for a non-symmetric coupling of interior penalty discontinuous Galerkin and boundary element methods in 2D and 3D, extending existing theory to a new method combination.
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-Nédeléc'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.