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Volume 29, Issue 2
Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation

Xianggui Li, Xijun Yu & Guangnan Chen

DOI: 10.4208/jcm.1009-m3113

J. Comp. Math., 29 (2011), pp. 227-242.

Published online: 2011-04

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  • 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.

  • Keywords

Convergence, Singular perturbation, Convection-diffusion equation, Finite element method.

  • AMS Subject Headings

65N30, 35J20.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-227, author = {Xianggui Li, Xijun Yu and Guangnan Chen}, title = {Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1009-m3113}, url = {http://global-sci.org/intro/article_detail/jcm/8475.html} }
TY - JOUR T1 - Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation AU - Xianggui Li, Xijun Yu & Guangnan Chen JO - Journal of Computational Mathematics VL - 2 SP - 227 EP - 242 PY - 2011 DA - 2011/04 SN - 29 DO - http://doi.org/10.4208/jcm.1009-m3113 UR - https://global-sci.org/intro/article_detail/jcm/8475.html KW - Convergence, Singular perturbation, Convection-diffusion equation, Finite element method. AB -

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.

Xianggui Li, Xijun Yu and Guangnan Chen. (2011). Error Estimates of the Finite Element Method with Weighted Basis Functions for a Singularly Perturbed Convection-Diffusion Equation. Journal of Computational Mathematics. 29 (2). 227-242. doi:10.4208/jcm.1009-m3113
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