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A mixed-FEM and BEM coupling for the approximation of the scattering of thermal wavesin locally non-homogeneous media

Published online by Cambridge University Press:  16 January 2007

María-Luisa Rapún  and
Francisco-Javier Sayas
María-Luisa Rapún
Affiliation:
Dep. Matemática e Informática, Universidad Pública de Navarra. Campus de Arrosadía, 31006 Pamplona, Spain.
Francisco-Javier Sayas
Affiliation:
Dep. Matemática Aplicada, Universidad de Zaragoza. C.P.S., 50018 Zaragoza, Spain.
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Abstract

This paper proposes and analyzes a BEM-FEM scheme to approximate a time-harmonic diffusion problem in the plane with non-constant coefficients in a bounded area. The model is set as a Helmholtz transmission problem with adsorption and with non-constant coefficients in a bounded domain. We reformulate the problem as a four-field system. For the temperature and the heat flux we use piecewise constant functions and lowest order Raviart-Thomas elements associated to a triangulation approximating the bounded domain. For the boundary unknowns we take spaces of periodic splines. We show how to transmit information from the approximate boundary to the exact one in an efficient way and prove well-posedness of the Galerkin method. Error estimates are provided and experimentally corroborated at the end of the work.

Keywords

Couplingfinite elementsboundary elementsexterior boundary value problemHelmholtz equation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 5 , September 2006 , pp. 871 - 896
Copyright
© EDP Sciences, SMAI, 2007

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