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Symmetric Coupling of LDG–FEM and DG–BEM

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Abstract

We analyze a discontinuous Galerkin FEM–BEM scheme for a second order elliptic transmission problem posed in the three-dimensional space. The symmetric variational formulation is discretized by nonconforming Raviart–Thomas finite elements on a general partition of the interior domain coupled with discontinuous boundary elements on an independent quasi-uniform mesh of the transmission interface. We prove (almost) quasi-optimal convergence of the method and confirm the theory by a numerical experiment. In addition we consider the case when continuous rather than discontinuous boundary elements are used.

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Authors and Affiliations

  1. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna, 4860, Santiago, Chile

    Norbert Heuer

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, Calvo Sotelo s/n, Oviedo, Spain

    Salim Meddahi

  3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Francisco-Javier Sayas

Authors
  1. Norbert Heuer
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  2. Salim Meddahi
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  3. Francisco-Javier Sayas
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Corresponding author

Correspondence to Salim Meddahi.

Additional information

Partial support by the following institutions is gratefully acknowledged: CONICYT through projects Anillo ACT1118 (ANANUM) and Fondecyt 1110324, Spain’s Ministry of Economy Project MTM2013-43671-P, and NSF through Grant DMS 1216356.

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Heuer, N., Meddahi, S. & Sayas, FJ. Symmetric Coupling of LDG–FEM and DG–BEM. J Sci Comput 68, 303–325 (2016). https://doi.org/10.1007/s10915-015-0139-8

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  • DOI: https://doi.org/10.1007/s10915-015-0139-8

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