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.