A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, p. 871-896

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.

DOI : https://doi.org/10.1051/m2an:2006033
Classification:  65J05,  65N30,  65N38,  65R20
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {5},
     year = {2006},
     pages = {871-896},
     doi = {10.1051/m2an:2006033},
     zbl = {1123.65115},
     mrnumber = {2293250},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 5, pp. 871-896. doi : 10.1051/m2an:2006033. http://www.numdam.org/item/M2AN_2006__40_5_871_0/

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