Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/55158
Title: The finite element method with weighted basis functions for singularly perturbed convectionâdiffusion problems
Authors: Li, XG
Chan, CK 
Wang, S
Keywords: Singular perturbation
Convectionâdiffusion equations
Finite element method
Flux approximation
Unstructured mesh
Issue Date: 2004
Publisher: Academic Press
Source: Journal of computational physics, 2004, v. 195, no. 2, p. 773-789 How to cite?
Journal: Journal of computational physics 
Abstract: In this paper, we present a finite element method for singularly perturbed convectionâdiffusion problems in both one and two dimensions, based on a set of weighted basis functions constructed on unstructured meshes (in 2D). For the one-dimensional case, both first and second-order schemes are discussed. A technique for approximating fluxes is proposed. Some theoretical results on uniform convergence are obtained. For the two-dimensional case, a first-order scheme is constructed for problems with two singular perturbation parameters. A technique is also developed in approximating fluxes in 2D. This technique is used to simplify the calculation of the integrals in the stiffness matrix arising from the scheme, which will save computational costs. The numerical results support the theoretical results and demonstrate that the method is stable for a wide range of singular perturbation parameters.
URI: http://hdl.handle.net/10397/55158
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2003.10.028
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