Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems

作者：

Highlights：

• For singularly perturbed problems with two parameters, we obtain the uniform convergence in the balanced norm of any order finite element method on a Shishkin mesh.

• We use Lagrange interpolation as a bridge to skillfully analyze the error estimation of L2-projection.

摘要

•For singularly perturbed problems with two parameters, we obtain the uniform convergence in the balanced norm of any order finite element method on a Shishkin mesh.•We use Lagrange interpolation as a bridge to skillfully analyze the error estimation of L2-projection.

论文关键词：Shishkin mesh,Two parameters,Balanced norm,Singular perturbation,Finite element method

论文评审过程：Received 24 November 2021, Revised 7 April 2022, Accepted 7 June 2022, Available online 25 June 2022, Version of Record 25 June 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127315