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A nonconforming exponentially fitted finite element method for two‐dimensional drift‐diffusion models in semiconductors
Author(s) -
Sacco Riccardo,
Gatti Emilio,
Gotusso Laura
Publication year - 1999
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199903)15:2<133::aid-num1>3.0.co;2-n
Subject(s) - mathematics , finite element method , convection–diffusion equation , mathematical analysis , partial differential equation , norm (philosophy) , discontinuous galerkin method , triangulation , divergence (linguistics) , galerkin method , convergence (economics) , current (fluid) , diffusion , exponential growth , geometry , physics , law , linguistics , philosophy , political science , economics , thermodynamics , economic growth
A new nonconforming exponentially fitted finite element for a Galerkin approximation of convection–diffusion equations with a dominating advective term is considered. The attention is here focused on the drift‐diffusion current continuity equations in semiconductor device modeling. The scheme extends to the two‐dimensional case, the well known Scharfetter–Gummel method, by imposing a divergence‐free current over each element of the triangulation. Convergence of the method in the energy norm is proved and some numerical results are included. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 133–150, 1999