IJPAM: Volume 14, No. 1 (2004)

A NEW MIXED-HYBRID FINITE ELEMENT
METHOD FOR CONVECTION-DIFFUSION PROBLEMS

A. Serghini Mounim
Department of Mathematics and Statistics
University of Moncton
Moncton, N.-B., E1A 3E9, CANADA


Abstract.In this paper we propose a mixed hybrid finite element method for solving convection-diffusion problems in one space dimension. The method combines a framework of mixed methods, and finite volume philosophy. We derive a new formulation of the convection-diffusion problem in which the general flux is introduced as new variable, and the local conservation is achieved, using the procedure, which consists to impose the continuity conditions of the general flux by means of a Lagrange multiplier. The practicality of the approach relies on a choice of local basis, presented here for the functional discrete subspace of the conserved quantity, consequently, the stabilizing mechanism is intrinsically contained in the trial finite element space. The choice of shape functions is inspired by the problem structure. One of the advantages of the scheme is the upwinding introduced by the basis functions, unlike the usual hat functions, which give a centered schemes. Furthermore, we show particularly its relationship with the most popular scheme for semiconductor problems, in the circumstances, the Scharfetter and Gummel scheme [#!SG!#]. We also perform some numerical tests, showing the advantages of the scheme.

Received: April 27, 2004

AMS Subject Classification: 73V05, 76M10, 65L60, 65M60

Key Words and Phrases: mixed hybrid finite element method, finite volume scheme, convection-diffusion problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 1