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IMA Journal of Numerical Analysis Advance Access originally published online on January 21, 2008
IMA Journal of Numerical Analysis 2008 28(3):469-495; doi:10.1093/imanum/drm030
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods

Abdallah Bradji{dagger}

Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany

Raphaèle Herbin{ddagger}

Laboratoire d'Analyse, Topologie et Probabilités, 6632, Université de Marseille, 39 rue F. Joliot Curie, 13453 Marseille, France

{dagger} Email: bradji{at}wias-berlin.de

{ddagger} Corresponding author. Email: herbin{at}latp.univ-mrs.fr

Received on 8 January 2007. Accepted for publication 21 July 2007.


  Abstract

We consider a nonlinear system of elliptic equations, which arises when modelling the heat diffusion problem coupled with the electrical diffusion problem. The ohmic losses which appear as a source term in the heat diffusion equation yield a nonlinear term which couples the equations. A finite-element scheme and a finite-volume scheme are considered for the discretization of the system; in both cases, we show that the approximate solution obtained with the scheme converges, up to a subsequence, to a solution of the coupled elliptic system.

Key Words: nonlinear elliptic system; diffusion equation; finite-element scheme; finite-volume scheme; L1-data; ohmic losses


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