A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation

Authors:
Song Wang;Zi-Cai Li
Affiliations:
Department of Mathematics & Statistics, The University of Western Australia, 35, Stirling Highway, Crawley, Western Australia 6009, Australia;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan
Venue:
Mathematics of Computation
Year:
2003

Citing 4
Cited 4

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Accurate and approximate analytic solutions of singularly perturbed differential equations with two-dimensional boundary layers

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Error estimates for a finite element-finite volume discretization of convection-diffusion equations

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Abstract

In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ε. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular elements. It is shown that the method is stable with respect to a semi-discrete energy norm and the approximation error in the semi-discrete energy norm is bounded by Ch√|ln ε/ln h| with C independent of the mesh parameter h, the diffusion coefficient ε and the exact solution of the problem.