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We analyze a non-symmetric coupling of interior penalty discontinuousGalerkin and boundary element methods in two and three dimensions. Main resultsare discrete coercivity of the method, and thus unique solvability, andquasi-optimal convergence. The proof of coercivity is based on a localizedvariant of the variational technique from [F.-J. Sayas, The validity ofJohnson-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 termswhich are carefully analyzed in fractional order Sobolev spaces, and by usingscaling arguments for rigid transformations. Numerical evidence of the provenconvergence properties has been published previously.

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