Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation

Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation

Year:    2011

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 2 : pp. 227–242

Abstract

In this paper, we establish a convergence theory for a finite element method with weighted basis functions for solving singularly perturbed convection-diffusion equations. The stability of this finite element method is proved and an upper bound $\mathcal{O}(h|\ln \varepsilon |^{3/2})$ for errors in the approximate solutions in the energy norm is obtained on the triangular Bakhvalov-type mesh. Numerical results are presented to verify the stability and the convergent rate of this finite element method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1009-m3113

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 2 : pp. 227–242

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Convergence Singular perturbation Convection-diffusion equation Finite element method.

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