Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, p. 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 : https://doi.org/10.1051/m2an:2003028
Classification:  65M60,  76X05
Keywords: finite volume scheme, drift-diffusion equations, approximation of gradient
@article{M2AN_2003__37_2_319_0,
     author = {Chainais-Hillairet, Claire and Liu, Jian-Guo and Peng, Yue-Jun},
     title = {Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     pages = {319-338},
     doi = {10.1051/m2an:2003028},
     zbl = {1032.82038},
     mrnumber = {1991203},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2003__37_2_319_0}
}
Chainais-Hillairet, Claire; Liu, Jian-Guo; Peng, Yue-Jun. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, pp. 319-338. doi : 10.1051/m2an:2003028. http://www.numdam.org/item/M2AN_2003__37_2_319_0/

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