An analysis of the weak Galerkin finite element method for convection-diffusion equations

被引：12
|
作者：
Zhang, Tie [1 ]
Chen, Yanli [1 ]
机构：
[1] Northeastern Univ, Dept Math, Shenyang 110004, Liaoning, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2019年 / 346卷
基金：
中国国家自然科学基金;
关键词：
Weak Galerkin method; Optimal error estimate; Superconvergence; Convection-diffusion equation;
D O I：
10.1016/j.amc.2018.10.064
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the weak finite element method solving convection-diffusion equations. A new weak finite element scheme is presented based on a special variational form. The optimal order error estimates are derived in the discrete H-1-norm, the L-2-norm and the L-infinity-norm, respectively. In particular, the H-1-superconvergence of order k + 2 is obtained under certain condition if polynomial pair P-k(K) x Pk+1 (partial derivative K) is used in the weak finite element space. Finally, numerical examples are provided to illustrate our theoretical analysis. (C) 2018 Elsevier Inc. All rights reserved.
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页码：612 / 621
页数：10
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