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

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 KW - Singular perturbation KW - Convection-diffusion equation KW - 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 & Guangnan Chen. (1970). 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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