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

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- by Song Wang and Zi-Cai Li;
- Math. Comp.
**72**(2003), 1689-1709 - DOI: https://doi.org/10.1090/S0025-5718-03-01516-3
- Published electronically: 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 $\displaystyle C h\sqrt {\left | \frac {\ln \varepsilon }{\ln h}\right |}$ with $C$ independent of the mesh parameter $h$, the diffusion coefficient $\varepsilon$ and the exact solution of the problem.## References

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## Bibliographic Information

**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
**Zi-Cai Li**- Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424
- Email: zcli@math.nsysu.edu.tw
- Received by editor(s): June 7, 2001
- Received by editor(s) in revised form: December 28, 2001
- Published electronically: May 21, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp.
**72**(2003), 1689-1709 - MSC (2000): Primary 65N30; Secondary 76M10
- DOI: https://doi.org/10.1090/S0025-5718-03-01516-3
- MathSciNet review: 1986800