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Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters
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- Journal:
- Advances in Applied Mathematics and Mechanics / Volume 7 / Issue 2 / April 2015
- Published online by Cambridge University Press:
- 10 March 2015, pp. 196-206
- Print publication:
- April 2015
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- Article
- Export citation
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In this paper, we consider a singularly perturbed convection-diffusion problem. The problem involves two small parameters that gives rise to two boundary layers at two endpoints of the domain. For this problem, a non-monotone finite element methods is used. A priori error bound in the maximum norm is obtained. Based on the a priori error bound, we show that there exists Bakhvalov-type mesh that gives optimal error bound of
(N−2) which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.
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