A MODIFIED WEAK GALERKIN FINITE ELEMENTMETHOD FOR SINGULARLY PERTURBED PARABOLIC CONVECTION-DIFFUSION-REACTION PROBLEMS  

作　　者：Suayip Toprakseven Fuzheng Gao 

机构地区：[1]Faculty of Engineering,Department of Computer Science,Artvin Coruh University,Artvin,08100,Turkey [2]School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Journal of Computational Mathematics》2023年第6期1246-1280,共35页计算数学（英文）

基　　金：supported in part by National Natural Science Foundation of China (No.11871038).

摘　　要：In this work,a modified weak Galerkin finite element method is proposed for solving second order linear parabolic singularly perturbed convection-diffusion equations.The key feature of the proposed method is to replace the classical gradient and divergence operators by the modified weak gradient and modified divergence operators,respectively.We apply the backward finite difference method in time and the modified weak Galerkin finite element method in space on uniform mesh.The stability analyses are presented for both semi-discrete and fully-discrete modified weak Galerkin finite element methods.Optimal order of convergences are obtained in suitable norms.We have achieved the same accuracy with the weak Galerkin method while the degrees of freedom are reduced in our method.Various numerical examples are presented to support the theoretical results.It is theoretically and numerically shown that the method is quite stable.

关 键 词：The modified weak Galerkin finite element method Backward Euler method Parabolic convection-diffusion problems Error estimates 

分 类 号：O241.82[理学—计算数学]