Some recent advances on vertex centered finite volume element methods for elliptic equations

In this paper, we report our recent advances on vertex centered finite volume element methods (FVEMs) for second order partial differential equations (PDEs). We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of ar...

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Bibliographic Details
Published inScience China. Mathematics Vol. 56; no. 12; pp. 2507 - 2522
Main Authors Zhang, ZhiMin, Zou, QingSong
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2013
Subjects
Applications of Mathematics
China
Construction
Error analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Partial differential equations
Positioning
Reviews
inf-sup condition
Secondary 45N08
finite volume method
high order
Primary 65N30
superconvergence
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Summary:In this paper, we report our recent advances on vertex centered finite volume element methods (FVEMs) for second order partial differential equations (PDEs). We begin with a brief review on linear and quadratic finite volume schemes. Then we present our recent advances on finite volume schemes of arbitrary order. For each scheme, we first explain its construction and then perform its error analysis under both H 1 and L 2 norms along with study of superconvergence properties.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-013-4740-8