Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
Laboratoire de Mathématiques Appliquées, CNRS UMR 6620,
Université Blaise Pascal (Clermont-Ferrand 2),
63177 Aubière Cedex, France.
2 Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA. email@example.com.
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.
Mathematics Subject Classification: 65M60 / 76X05
Key words: Finite volume scheme / drift-diffusion equations / approximation of gradient.
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