Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

被引：5
作者：
Chen, Yanli [1 ]
Li, Yonghai [2 ]
机构：
[1] Jilin Univ, Inst Math, Changchun 130012, Peoples R China
[2] Jilin Univ, Sch Math, Changchun 130012, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2015年 / 7卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Finite volume method; bicubic element; quadrilateral meshes; ELEMENT METHOD; COVOLUME; SUPERCONVERGENCE; CONVERGENCE; SCHEMES;
D O I：
10.4208/aamm.2013.m401
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called element wise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal O(h(3)) convergence rate in H-1 norm. Additionally, we apply this analysis technique to bilinear finite volume method. Finally, numerical examples are provided to confirm the theoretical analysis of bicubic finite volume method.
引用
收藏
页码：454 / 471
页数：18
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