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Finite volume scheme for multi-dimensionaldrift-diffusion equations and convergence analysis

Published online by Cambridge University Press:  15 November 2003

Claire Chainais-Hillairet ,
Jian-Guo Liu  and
Yue-Jun Peng
Claire Chainais-Hillairet
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177 Aubière Cedex, France. chainais@math.univ-bpclermont.fr., peng@math.univ-bpclermont.fr.
Jian-Guo Liu
Affiliation:
Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA. jliu@math.umd.edu.
Yue-Jun Peng
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177 Aubière Cedex, France. chainais@math.univ-bpclermont.fr., peng@math.univ-bpclermont.fr.
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Abstract

We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal with coupled terms in the continuity equations. Finally, a numerical example is given to show the efficiency of the scheme.

Keywords

Finite volume schemedrift-diffusion equationsapproximation of gradient.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 319 - 338
Copyright
© EDP Sciences, SMAI, 2003

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