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Admissible Regions for Higher-Order Finite Volume Method Grids

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  02 May 2017

Yuanyuan Zhang  and
Zhongying Chen
Yuanyuan Zhang*
Affiliation:
Department of Mathematics and Information Science, Yantai University, Yantai 264005, China
Zhongying Chen*
Affiliation:
Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Sciences, Sun Yat-sen University, Guangzhou 510275, China
*
*Corresponding author. Email addresses:yy0dd@126.com (Y. Zhang), lnsczy@mail.sysu.edu.cn (Z. Chen)
*Corresponding author. Email addresses:yy0dd@126.com (Y. Zhang), lnsczy@mail.sysu.edu.cn (Z. Chen)
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Abstract

Admissible regions for higher-order finite volume method (FVM) grids are considered. A new Hermite quintic FVM and a new hybrid quintic FVM are constructed to solve elliptic boundary value problems, and the corresponding admissible regions are investigated. A sufficient condition for the uniform local-ellipticity of the new hybrid quintic FVM is obtained when its admissible region is known. In addition, the admissible regions for a large number of higher-order FVMs are provided. For the same class of FVM (Lagrange, Hermite or hybrid), the higher order FVM has a smaller admissible region such that stronger geometric restrictions are required to guarantee its uniform local-ellipticity.

Keywords

Finite volume methodadmissible regionuniform local-ellipticity

MSC classification

Secondary: 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N12: Stability and convergence of numerical methods
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 269 - 285
Copyright
Copyright © Global-Science Press 2017 

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