Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh

作者：

Highlights：

• We consider a two-dimension singularly perturbed elliptic problem with two parameters.

• We combine the characteristics of the mesh and the layers to choose technical tools for error analysis.

• Using some important integral inequalities, we prove the convergence and supercloseness of finite element method on Shishkin triangular mesh.

摘要

•We consider a two-dimension singularly perturbed elliptic problem with two parameters.•We combine the characteristics of the mesh and the layers to choose technical tools for error analysis.•Using some important integral inequalities, we prove the convergence and supercloseness of finite element method on Shishkin triangular mesh.

论文关键词：Singular perturbation,Uniform convergence,Finite element method,Shishkin triangular mesh,Supercloseness,Two parameters

论文评审过程：Received 24 May 2021, Revised 13 October 2021, Accepted 25 October 2021, Available online 10 November 2021, Version of Record 10 November 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126753