THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D  

作　　者：Chunxiao ZHANG Jin ZHANG 张春晓;张进(School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China)

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China

出　　处：《Acta Mathematica Scientia》2024年第4期1572-1593,共22页数学物理学报（B辑英文版）

基　　金：supported by National Natural Science Foundation of China(11771257);the Shandong Provincial Natural Science Foundation of China(ZR2023YQ002,ZR2023MA007,ZR2021MA004)。

摘　　要：For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.

关 键 词：singularly perturbed CONVECTION-DIFFUSION finite element method SUPERCLOSENESS Bakhvalov-type mesh 

分 类 号：O241.82[理学—计算数学]