Supercloseness of finite element method on a Bakhvalov-type mesh for a singularly perturbed problem with two parameters

摘要

In this paper, the linear finite element method on a Bakhvalov-type mesh is applied to a singularly perturbed problem with two parameters. There is a strong exponential boundary layer and a weak exponential boundary layer in the solution of this problem. In the analysis, we discuss three cases and obtain the corresponding uniform convergence and supercloseness results by using different analysis techniques. Numerical tests confirm our theoretical results.