# 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 (2010)

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

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topChainais-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 37.2 (2010): 319-338. <http://eudml.org/doc/194165>.

@article{Chainais2010,

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},

keywords = {Finite volume scheme; drift-diffusion equations; approximation of gradient.; finite volume scheme; approximation of gradient},

language = {eng},

month = {3},

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/194165},

volume = {37},

year = {2010},

}

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

DA - 2010/3//

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.; finite volume scheme; approximation of gradient

UR - http://eudml.org/doc/194165

ER -

## References

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