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On the Discretization of the Coupled Heat and Electrical Diffusion Problems

  • Abdallah Bradji
  • Raphaèle Herbin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4310)

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 lies in L 1. A finite volume scheme is proposed for the discretization of the system; we show that the approximate solution obtained with the scheme converges, up to a subsequence, to a solution of the coupled elliptic system.

Keywords

Nonlinear elliptic system Diffusion equation Finite volume scheme L1-data Ohmic losses 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Abdallah Bradji
    • 1
  • Raphaèle Herbin
    • 2
  1. 1.Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39 10117 BerlinGermany
  2. 2.Laboratoire d’Analyse, Topologie et Probabilités, Université Aix–Marseille 1, 39 rue Joliot Curie 13453 MarseilleFrance

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