An analysis of a conforming exponentially fitted finite element method for a convection-diffusion problem

Authors:
Song Wang;Zi-Cai Li
Affiliations:
Department of Mathematics and Statistics, The University of Western Australia, Nedlands, WA 6907, Australia;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

In this paper, we present a convergence analysis for a conforming exponentially fitted Galerkin finite element method with triangular elements for a linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. It is shown that the error for the finite element solution in the energy norm is bounded by O(h(ε1/2||u||2+ε-1/2||u||1)) if a regular family of triangular meshes is used. In the case that a problem contains only exponential boundary layers, the method is shown to be convergent at a rate of h1/2 + h|ln ε| on anisotropic layer-fitted meshes.