Analysis of a non-symmetric coupling of Interior Penalty DG and BEM
Norbert Heuer and Francisco-Javier Sayas
Math. Comp. 84 (292), 581-598, 2015.
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, SIAM J. Numer. Anal., 47(5):3451-3463, 2009].
This localization gives rise to terms which a re 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.