Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-Hillairet; Jian-Guo Liu; Yue-Jun Peng

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 2, page 319-338
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Chainais-Hillairet, Claire, Liu, Jian-Guo, and 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 37.2 (2003): 319-338. <http://eudml.org/doc/244819>.

@article{Chainais2003,
abstract = {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.},
author = {Chainais-Hillairet, Claire, Liu, Jian-Guo, Peng, Yue-Jun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite volume scheme; drift-diffusion equations; approximation of gradient},
language = {eng},
number = {2},
pages = {319-338},
publisher = {EDP-Sciences},
title = {Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis},
url = {http://eudml.org/doc/244819},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Chainais-Hillairet, Claire
AU - Liu, Jian-Guo
AU - Peng, Yue-Jun
TI - Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 2
SP - 319
EP - 338
AB - 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.
LA - eng
KW - finite volume scheme; drift-diffusion equations; approximation of gradient
UR - http://eudml.org/doc/244819
ER -

References

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