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.
Mots clés : coupling, finite elements, boundary elements, exterior boundary value problem, Helmholtz equation
@article{M2AN_2006__40_5_871_0, author = {Rap\'un, Mar{\'\i}a-Luisa and Sayas, Francisco-Javier}, title = {A {mixed-FEM} and {BEM} coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {871--896}, publisher = {EDP-Sciences}, volume = {40}, number = {5}, year = {2006}, doi = {10.1051/m2an:2006033}, mrnumber = {2293250}, zbl = {1123.65115}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2006033/} }
TY - JOUR AU - Rapún, María-Luisa AU - Sayas, Francisco-Javier TI - A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 871 EP - 896 VL - 40 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006033/ DO - 10.1051/m2an:2006033 LA - en ID - M2AN_2006__40_5_871_0 ER -
%0 Journal Article %A Rapún, María-Luisa %A Sayas, Francisco-Javier %T A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 871-896 %V 40 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006033/ %R 10.1051/m2an:2006033 %G en %F M2AN_2006__40_5_871_0
Rapún, María-Luisa; Sayas, Francisco-Javier. A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 5, pp. 871-896. doi : 10.1051/m2an:2006033. http://www.numdam.org/articles/10.1051/m2an:2006033/
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