Mathematics of Computation

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

Author(s): Song Wang; Zi-Cai Li.
Journal: Math. Comp. 72 (2003), 1689-1709.
MSC (2000): Primary 65N30; Secondary 76M10
Posted: May 21, 2003
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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 $\varepsilon$ . 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 $\displaystyle C h\sqrt{\left \vert \frac{\ln \varepsilon}{\ln h}\right \vert}$ with

independent of the mesh parameter

, the diffusion coefficient $\varepsilon$ and the exact solution of the problem.

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Song Wang
Affiliation: Department of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia
Email: swang@maths.uwa.edu.au

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