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A Petrov‐Galerkin mixed finite element method with exponential fitting
Author(s) -
Van Nooyen R. R. P.
Publication year - 1995
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/num.1690110507
Subject(s) - mathematics , petrov–galerkin method , finite element method , discretization , estimator , degenerate energy levels , discontinuous galerkin method , a priori and a posteriori , exponential function , galerkin method , domain (mathematical analysis) , mathematical analysis , mixed finite element method , philosophy , statistics , physics , epistemology , quantum mechanics , thermodynamics
We discuss a Petrov‐Galerkin mixed finite element formulation of the semiconductor continuity equations on a rectangular domain. We give error estimates for equations that are in principle degenerate in the singularly perturbed case. We give arguments that indicate that the method is also effective in the singularly perturbed case. We develop a discretization that gives a higher‐order accurate solution for use in an a posteriori error estimator. © 1995 John Wiley & Sons, Inc.