A triangular mixed finite element method for the stationary semiconductor device equations

On presente ici une methode d'elements finis mixte, de type Petrov-Galerkin, basee sur des elements triangulaires, pour un systeme elliptique auto-adjoint du second ordre, emanant d'un modele stationnaire pour des semiconducteurs. Cette methode est basee sur une nouvelle formulation du probleme discret correspondant et peut etre consideree comme une extension bidimensionnelle naturelle de la methode bien connue de Scharfetter-Gummel. L'existence, l'unicite et la stabilite de la solution approchee sont etablies pour un maillage triangulaire arbitraire et une estimation de l'erreur est donnee pour une triangulation de Delaunay arbitraire et sa tesselation de Dirichlet

[1]  B. Heinrich.  Finite Difference Methods on Irregular Networks , 1987 .

[2]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[3]  Tsutomu Ikeda,et al.  Maximum Principle in Finite Element Models for Convection-diffusion Phenomena , 1983 .

[4]  I. Babuska,et al.  Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods , 1983 .

[5]  A. Aziz.  The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations , 1972 .

[6]  Peter A. Markowich,et al.  Inverse-average-type nite element discretizations of self-adjoint second order elliptic problems , 1988 .

[7]  H. Gummel.  A self-consistent iterative scheme for one-dimensional steady state transistor calculations , 1964 .

[8]  P. G. Ciarlet,et al.  General lagrange and hermite interpolation in Rn with applications to finite element methods , 1972 .

[9]  C. H. Wu,et al.  A mixed finite element method for the stationary semiconductor continuity equations , 1988 .

[10]  J. T. Oden,et al.  Theory of mixed and hybrid finite-element approximations in linear elasticity , 1976 .

[11]  P. Raviart,et al.  Finite Element Approximation of the Navier-Stokes Equations , 1979 .

[12]  E. M. Buturla,et al.  Finite-element analysis of semiconductor devices: the FIELDAY program , 1981 .

[13]  Paola Pietra,et al.  Two-dimensional exponential fitting and applications to drift-diffusion models , 1989 .

[14]  M. S. Mock,et al.  ANALYSIS OF A DISCRETIZATION ALGORITHM FOR STATIONARY CONTINUITY EQUATIONS IN SEMICONDUCTOR DEVICE MODELS, II , 1983 .

[15]  Li Ronghua,et al.  Generalized difference methods for a nonlinear Dirichlet problem , 1987 .

[16]  M. ButurlaE.,et al.  Finite-element analysis of semiconductor devices , 1981 .

[17]  Roland Glowinski,et al.  An introduction to the mathematical theory of finite elements , 1976 .

[18]  R. H. MacNeal,et al.  An asymmetrical finite difference network , 1953 .

[19]  G. L. Dirichlet.  Über die Reduction der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. , 1850 .

[20]  W. V. Roosbroeck.  Theory of the flow of electrons and holes in germanium and other semiconductors , 1950 .