ERROR ESTIMATES OF THE FINITE ELEMENT METHOD WITH WEIGHTED BASIS FUNCTIONS FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATION

作     者：Xianggui Li Xijun Yu Guangnan Chen 

作者机构：School of Applied Science Beijing Information Science and Technology University Beijing 100101 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2011年第29卷第2期

页      面：227-242页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work is supported by National Natural Science Foundation of China (NSFC10671023) and Beijing Municipal Education Commission (71D0911003). The second author acknowledges the support from National Natural Science Foundation of China (NSFC10771019) 

主　　题：Convergence Singular perturbation Convection-diffusion equation Finite element method. 

摘      要：In this paper, we establish a convergence theory for a finite element method with weighted basis functions for solving singularly perturbed convection-diffusion equations. The stability of this finite element method is proved and an upper bound O（h｜lnε｜3/2） for errors in the approximate solutions in the energy norm is obtained on the triangular Bakhvalov-type mesh. Numerical results are presented to verify the stability and the convergent rate of this finite element method.