Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 319-338.

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.

DOI : 10.1051/m2an:2003028
Classification : 65M60, 76X05
Mots-clés : finite volume scheme, drift-diffusion equations, approximation of gradient 
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     title = {Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {319--338},
     publisher = {EDP-Sciences},
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Chainais-Hillairet, Claire; Liu, Jian-Guo; Peng, Yue-Jun. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 319-338. doi : 10.1051/m2an:2003028. http://www.numdam.org/articles/10.1051/m2an:2003028/

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