Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model |
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Authors: | Chainais-Hillairet Claire; Filbet Francis |
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Institution: |
Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand, 24 Avenue des Landais, 63177 Aubière cedex, France
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Abstract: |
Francis Filbet
Université de Lyon, Université Lyon 1, CNRS, UMR 5208, Institut Camille Jordan, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France
Received on 28 June 2006. Revised on 6 December 2006. In this paper, we propose a finite-volume discretization formultidimensional nonlinear drift-diffusion system. Such a systemarises in semiconductors modelling and is composed of two parabolicequations and an elliptic one. We prove that the numerical solutionconverges to a steady state when time goes to infinity. Severalnumerical tests show the efficiency of the method. |
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Keywords: | drift-diffusion system thermal equilibrium boundary problem finite-volume scheme |
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