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

Mathematical Modelling and Numerical Analysis

Volumn 37, Issue 2, 2003, Pages 319-338

  Chainais Hillairet, Claire ^a   Liu, Jian Guo ^b   Peng, Yue Jun ^a  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b Bldg 142   (United States)

Author keywords

Approximation of gradient; Drift diffusion equations; Finite volume scheme

Indexed keywords

EID: 0038649265     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2003028     Document Type: Article

References (19)

1. F. Arimburgo, C. Baiocchi and L.D. Marini, Numerical approximation of the 1-D nonlinear drift-diffusion model in semiconductors, in Nonlinear kinetic theory and mathematical aspects of hyperbolic systems, Rapallo, (1992) 1-10. World Sci. Publishing, River Edge, NJ (1992).
2. H. Beirão da Veiga, On the semiconductor drift diffusion equations. Differential Integral Equations 9 (1996) 729-744.
3. H. Brezis, Analyse Fonctionnelle - Théorie et Applications. Masson, Paris (1983).
4. F. Brezzi, L.D. Marini and P. Pietra, Méthodes d'éléments finis mixtes et schéma de Scharfetter-Gummel. C. R. Acad. Sci. Paris Sér. I Math. 305 (1987) 599-604.
5. F. Brezzi, L.D. Marini and P. Pietra, Two-dimensional exponential fitting and applications to drift-diffusion models. SIAM J. Numer. Anal. 26 (1989) 1342-1355.
6. C. Chainais-Hillairet and Y.J. Peng, Convergence of a finite volume scheme for the drift-diffusion equations in 1-D. IMA J. Numer. Anal. 23 (2003) 81-108.
7. C. Chainais-Hillairet and Y.J. Peng, A finite volume scheme to the drift-diffusion equations for semiconductors, in Proc. of The Third International Symposium on Finite Volumes for Complex Applications, R. Herbin and D. Kröner Eds., Hermes, Porquerolles, France (2002) 163-170.
8. C. Chainais-Hillairet and Y.J. Peng, Finite volume approximation for degenerate drift-diffusion system in several space dimensions. Math. Models Methods. Appl. Sci. (submitted).
9. P.O. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978).
10. R. Eymard, T. Gallouët and R. Herbin, Finite Volume Methods. North-Holland, Amsterdam, Handb. Numer. Anal. VII (2000) 713-1020.
11. R. Eymard, T. Gallouët, R. Herbin and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations. Numer. Math. 92 (2002) 41-82,
12. W. Fang and K. Ito, Global solutions of the time-dependent drift-diffusion semiconductor equations. J. Differential Equations 123 (1995) 523-566.
13. H. Gajewski, On the uniqueness of solutions to the drift-diffusion model of semiconductor devices. Math. Models Methods Appl. Sci. 4 (1994) 121-133.
14. A. Jungel, Numerical approximation of a drift-diffusion model for semiconductors with nonlinear diffusion. ZAMM Z. Angew. Math. Mech. 75 (1995) 783-799.
15. A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling. Math. Nachr. 185 (1997) 85-110.
16. A. Jüngel and Y.J. Peng, A hierarchy of hydrodynamic models for plasmas: zero-relaxation-time limits. Comm. Partial Differential Equations 24 (1999) 1007-1033.
17. A. Jüngel and Y.J. Peng, Zero-relaxation-time limits in the hydrodynamic equations for plasmas revisited. Z. Angew. Math. Phys. 51 (2000) 385-396.
18. A. Jüngel and P, Pietra, A discretization scheme for a quasi-hydrodynamic semiconductor model. Math. Models Methods Appl. Sci. 7 (1997) 935-955.
19. P.A. Markowich, C.A. Ringhofer and C. Schmeiser, Semiconductor Equations. Springer-Verlag, Vienna (1990).