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

María-Luisa Rapún; Francisco-Javier Sayas[1]

  • [1] Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 3–50015 Zaragoza, Spain.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2006)

  • Volume: 40, Issue: 5, page 871-896
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Rapún, María-Luisa, and 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 40.5 (2006): 871-896. <http://eudml.org/doc/244801>.

@article{Rapún2006,
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.},
affiliation = {Dep. Matemática Aplicada, Universidad de Zaragoza, Centro Politécnico Superior, c/ María de Luna, 3–50015 Zaragoza, Spain.},
author = {Rapún, María-Luisa, Sayas, Francisco-Javier},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {coupling; finite elements; boundary elements; exterior boundary value problem; Helmholtz equation; thermal waves; scattering; non-homogeneous media; finite element method (FEM); boundary element method (BEM); Galerkin method; well-posedness; stability; convergence; non-destructing testing; numerical examples; time-harmonic diffusion problem; Helmholtz transmission problem},
language = {eng},
number = {5},
pages = {871-896},
publisher = {EDP-Sciences},
title = {A mixed-FEM and BEM coupling for the approximation of the scattering of thermal waves in locally non-homogeneous media},
url = {http://eudml.org/doc/244801},
volume = {40},
year = {2006},
}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2006
PB - EDP-Sciences
VL - 40
IS - 5
SP - 871
EP - 896
AB - 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.
LA - eng
KW - coupling; finite elements; boundary elements; exterior boundary value problem; Helmholtz equation; thermal waves; scattering; non-homogeneous media; finite element method (FEM); boundary element method (BEM); Galerkin method; well-posedness; stability; convergence; non-destructing testing; numerical examples; time-harmonic diffusion problem; Helmholtz transmission problem
UR - http://eudml.org/doc/244801
ER -

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