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Volume 7, Issue 2
Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters

Yanping Chen, Haitao Leng & Li-Bin Liu

DOI: 10.4208/aamm.2013.m399

Adv. Appl. Math. Mech., 7 (2015), pp. 196-206.

Published online: 2018-05

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  • Abstract

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 $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

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@Article{AAMM-7-196, author = {Chen , YanpingLeng , Haitao and Liu , Li-Bin}, title = {Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {2}, pages = {196--206}, abstract = {

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 $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m399}, url = {http://global-sci.org/intro/article_detail/aamm/12044.html} }
TY - JOUR T1 - Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters AU - Chen , Yanping AU - Leng , Haitao AU - Liu , Li-Bin JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 196 EP - 206 PY - 2018 DA - 2018/05 SN - 7 DO - http://doi.org/10.4208/aamm.2013.m399 UR - https://global-sci.org/intro/article_detail/aamm/12044.html KW - AB -

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 $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation parameters. Numerical results are given that confirm the theoretical result.

Chen , YanpingLeng , Haitao and Liu , Li-Bin. (2018). Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters. Advances in Applied Mathematics and Mechanics. 7 (2). 196-206. doi:10.4208/aamm.2013.m399
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