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Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. (English) Zbl 1032.82038

Summary: 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.

MSC:

82D37 Statistical mechanics of semiconductors
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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