High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters
作者：
Highlights：
• We investigate a kth (k≥2) order finite element method on a Bakhvalov-type mesh for a two-parameter singularly perturbed two-point boundary value problem.
• The characteristics of Bakhvalov-type meshes are fully exploited for uniform convergence in the energy norm.
• A new interpolation is introduced, which has similar structure to Lagrange interpolation. With this new interpolation, we overcome the difficulty caused by transition points on Bakhvalov-type mesh, and obtain the optimal convergence order.
摘要
•We investigate a kth (k≥2) order finite element method on a Bakhvalov-type mesh for a two-parameter singularly perturbed two-point boundary value problem.•The characteristics of Bakhvalov-type meshes are fully exploited for uniform convergence in the energy norm.•A new interpolation is introduced, which has similar structure to Lagrange interpolation. With this new interpolation, we overcome the difficulty caused by transition points on Bakhvalov-type mesh, and obtain the optimal convergence order.
论文关键词：Singular perturbation,Convection–diffusion equation,Two parameters,Finite element method,Bakhvalov-type mesh
论文评审过程：Received 5 September 2020, Revised 20 December 2020, Accepted 3 January 2021, Available online 19 January 2021, Version of Record 19 January 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.125953
