
Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
Publication
, Journal Article
Chainais-Hillairet, C; Liu, JG; Peng, YJ
Published in: Mathematical Modelling and Numerical Analysis
January 1, 2003
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.
Duke Scholars
Published In
Mathematical Modelling and Numerical Analysis
DOI
ISSN
0764-583X
Publication Date
January 1, 2003
Volume
37
Issue
2
Start / End Page
319 / 338
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Chainais-Hillairet, C., Liu, J. G., & Peng, Y. J. (2003). Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Mathematical Modelling and Numerical Analysis, 37(2), 319–338. https://doi.org/10.1051/m2an:2003028
Chainais-Hillairet, C., J. G. Liu, and Y. J. Peng. “Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis.” Mathematical Modelling and Numerical Analysis 37, no. 2 (January 1, 2003): 319–38. https://doi.org/10.1051/m2an:2003028.
Chainais-Hillairet C, Liu JG, Peng YJ. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Mathematical Modelling and Numerical Analysis. 2003 Jan 1;37(2):319–38.
Chainais-Hillairet, C., et al. “Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis.” Mathematical Modelling and Numerical Analysis, vol. 37, no. 2, Jan. 2003, pp. 319–38. Scopus, doi:10.1051/m2an:2003028.
Chainais-Hillairet C, Liu JG, Peng YJ. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. Mathematical Modelling and Numerical Analysis. 2003 Jan 1;37(2):319–338.

Published In
Mathematical Modelling and Numerical Analysis
DOI
ISSN
0764-583X
Publication Date
January 1, 2003
Volume
37
Issue
2
Start / End Page
319 / 338
Related Subject Headings
- Numerical & Computational Mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics