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Nonsymmetric coupling of BEM and mixed FEM on polyhedral interfaces

Authors: Salim Meddahi, Francisco-Javier Sayas and Virginia Selgás
Journal: Math. Comp. 80 (2011), 43-68
MSC (2010): Primary 65N30
Published electronically: August 17, 2010
MathSciNet review: 2728971
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Abstract: In this paper we propose and analyze some new methods for coupling mixed finite element and boundary element methods for the model problem of the Laplace equation in free space or in the exterior of a bounded domain. As opposed to the existing methods, which use the complete matrix of operators of the Calderón projector to obtain a symmetric coupled system, we propose methods with only one integral equation. The system can be considered as a further generalization of the Johnson-Nédélec coupling of BEM-FEM to the case of mixed formulations in the bounded domain. Using some recent analytical tools we are able to prove stability and convergence of Galerkin methods with very general conditions on the discrete spaces and no restriction relating the finite and boundary element spaces. This can be done for general Lipschitz interfaces and in particular, the coupling boundary can be taken to be a Lipschitz polyhedron. Both the indirect and the direct approaches for the boundary integral formulation are explored.

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Additional Information

Salim Meddahi
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain

Francisco-Javier Sayas
Affiliation: Departamento de Matemática Aplicada, CPS, Universidad de Zaragoza, 50018 Zaragoza, Spain and School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Virginia Selgás
Affiliation: Departamento de Matemáticas, Universidad de A Coruña, Facultad de Informática, Campus de Elviña s/n, 15071 A Coruña, Spain

Keywords: Mixed FEM, BEM–FEM coupling, Lipschitz domains
Received by editor(s): May 13, 2009
Received by editor(s) in revised form: September 8, 2009
Published electronically: August 17, 2010
Additional Notes: The first author was partially supported by the Spanish MEC Project MTM2007-65088
The second author was partially supported by Spanish MEC Project MTM2007–63204 and Gobierno de Aragón (Grupo Consolidado PDIE)
The third author was partially supported the Spanish MEC project MTM2007-67596-C02-01 and Xunta de Galicia (PGIDIT07PXIB105257PR)
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.