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 - <p style="text-align: justify;">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&nbsp;$\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbation
parameters. Numerical results are given that confirm the theoretical result.</p>