Free access
Volume 37, Number 2, March/April 2003
Page(s) 319 - 338
Published online 15 November 2003
  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. Beir ao da Veiga, On the semiconductor drift diffusion equations. Differential Integral Equations 9 (1996) 729-744. [MathSciNet]
  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. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  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.G. 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. [CrossRef] [MathSciNet]
  12. W. Fang and K. Ito, Global solutions of the time-dependent drift-diffusion semiconductor equations. J. Differential Equations 123 (1995) 523-566. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  14. A. Jüngel, Numerical approximation of a drift-diffusion model for semiconductors with nonlinear diffusion. ZAMM Z. Angew. Math. Mech. 75 (1995) 783-799. [CrossRef]
  15. A. Jüngel, A nonlinear drift-diffusion system with electric convection arising in semiconductor and electrophoretic modeling. Math. Nachr. 185 (1997) 85-110. [MathSciNet]
  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. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  18. A. Jüngel and P. Pietra, A discretization scheme for a quasi-hydrodynamic semiconductor model. Math. Models Methods Appl. Sci. 7 (1997) 935-955. [CrossRef] [MathSciNet]
  19. P.A. Markowich, C.A. Ringhofer and C. Schmeiser, Semiconductor Equations. Springer-Verlag, Vienna (1990).

Recommended for you