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Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes

Published online by Cambridge University Press:  29 May 2015

Yanli Chen  and
Yonghai Li
Yanli Chen
Affiliation:
Institute of Mathematics, Jilin University, Changchun 130012, China
Yonghai Li*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, China
*
*Corresponding author. Email: chenyanli7532@sina.com (Y. L. Chen), yonghai@jlu.edu.cn (Y. H. Li)
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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 convergence rate in H1 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.

Keywords

65N3065N15Finite volume methodbicubic elementquadrilateral meshes

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Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 4 , August 2015 , pp. 454 - 471
Copyright
Copyright © Global-Science Press 2015 

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