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Mathematics of Computation

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

Authors: Norbert Heuer and Francisco-Javier Sayas
Journal: Math. Comp. 84 (2015), 581-598
MSC (2010): Primary 65N30, 65N38, 65N12, 65N15
Published electronically: October 30, 2014
MathSciNet review: 3290956
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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-Nédeléc’s BEM-FEM coupling on polygonal interfaces, 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.

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Additional Information

Norbert Heuer
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile
MR Author ID: 314970

Francisco-Javier Sayas
Affiliation: Department of Mathematical Sciences, University of Delaware, Ewing Hall, Newark, Delaware 19711
MR Author ID: 621885

Received by editor(s): November 9, 2011
Received by editor(s) in revised form: January 18, 2013
Published electronically: October 30, 2014
Additional Notes: The first author was partially supported by CONICYT through FONDECYT project 1110324 and Anillo ACT1118 (ANANUM)
The second author was partially supported by NSF grant DMS 1216356
Article copyright: © Copyright 2014 American Mathematical Society