Supercloseness of linear streamline diffusion finite element method on Bakhvalov-type mesh for singularly perturbed convection-diffusion equation in 1D

作者：

Highlights：

• A streamline diffusion finite element method is properly defined on a Bakhvalov-type mesh.

• The novel point about the definition of the stabilization parameter is the choice of a linear function, instead of a constant, for the last element mesh in the layer.

• By means of delicate analysis, supercloseness of order 2, except for a logarithm factor, is proven.

摘要

•A streamline diffusion finite element method is properly defined on a Bakhvalov-type mesh.•The novel point about the definition of the stabilization parameter is the choice of a linear function, instead of a constant, for the last element mesh in the layer.•By means of delicate analysis, supercloseness of order 2, except for a logarithm factor, is proven.

论文关键词：Singular perturbation,Convection-diffusion equation,Bakhvalov-type mesh,Streamline diffusion finite element method,Supercloseness

论文评审过程：Received 26 October 2021, Revised 25 March 2022, Accepted 15 May 2022, Available online 27 May 2022, Version of Record 27 May 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127258