Error Analysis for a Non-Monotone FEM for a Singularly Perturbed Problem with Two Small Parameters (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, we consider a singularly perturbed convection-diffusion problem.The problem involves two small parameters that gives rise to two boundary layersat two endpoints of the domain. For this problem, a non-monotone finite elementmethods is used. A priori error bound in the maximum norm is obtained. Based onthe a priori error bound, we show that there exists Bakhvalov-type mesh that givesoptimal error bound of $\mathcal{O}(N^{−2})$ which is robust with respect to the two perturbationparameters. Numerical results are given that confirm the theoretical result.