Year: 2015
Author: Yanli Chen, Yonghai Li
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 454–471
Abstract
In this paper, an optimal bicubic finite volume method is established and analyzed for elliptic equations on quadrilateral meshes. Base on the so-called elementwise stiffness matrix analysis technique, we proceed the stability analysis. It is proved that the new scheme has optimal $\mathcal{O}(h^3)$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m401
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 454–471
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Author Details
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