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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Analysis of a non-symmetric coupling of Interior Penalty DG and BEM
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by Norbert Heuer and Francisco-Javier Sayas PDF
Math. Comp. 84 (2015), 581-598 Request permission

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
  • Email: nheuer@mat.puc.cl
  • Francisco-Javier Sayas
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Ewing Hall, Newark, Delaware 19711
  • MR Author ID: 621885
  • Email: fjsayas@udel.edu
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 581-598
  • MSC (2010): Primary 65N30, 65N38, 65N12, 65N15
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02918-9
  • MathSciNet review: 3290956