A discontinuous finite volume element method for second-order elliptic problems

被引：30
作者：
Bi, Chunjia [1 ]
Liu, Mingming [1 ]
机构：
[1] Yantai Univ, Dept Math, Yantai 264005, Shandong, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 28卷 / 02期
基金：
中国国家自然科学基金;
关键词：
discontinuous finite volume element method; elliptic problems; error estimates; the interior penalty method; GALERKIN METHODS; UNIFIED ANALYSIS; SUPERCONVERGENCE; PENALTY;
D O I：
10.1002/num.20626
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we propose a new discontinuous finite volume element (DFVE) method for the second-order elliptic problems. We treat the DFVE method as a perturbation of the interior penalty method and get a superapproximation estimate in a mesh dependent norm between the solution of the DFVE method and that of the interior penalty method. This reveals that the DFVE method is much closer to the interior penalty method than we have known. By using this superapproximation estimate, we can easily get the optimal order error estimates in the L2 -norm and in the maximum norms of the DFVE method.(c) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 425440, 2012
引用
收藏
页码：425 / 440
页数：16
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