Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D

作者：

Highlights：

• We present a weak Galerkin finite element method, exploring polynomial approximations of various degree, for solving singularly perturbed convection-diffusion equation in 2D.

• A special interpolation is delicately designed according to the structures of the designed method and Shishkin mesh. Uniform convergence of optimal order is proved.

摘要

•We present a weak Galerkin finite element method, exploring polynomial approximations of various degree, for solving singularly perturbed convection-diffusion equation in 2D.•A special interpolation is delicately designed according to the structures of the designed method and Shishkin mesh. Uniform convergence of optimal order is proved.

论文关键词：Convection-diffusion equation,Shishkin mesh,Weak Galerkin finite element method

论文评审过程：Received 17 April 2022, Revised 7 June 2022, Accepted 17 June 2022, Available online 4 July 2022, Version of Record 4 July 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127346