Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 269–285
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.290416.161016a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 269–285
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Finite volume method admissible region uniform local-ellipticity.
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A family of quadratic finite volume element schemes for anisotropic diffusion problems on triangular meshes
Zhou, Yanhui
Wu, Jiming
Journal of Computational and Applied Mathematics, Vol. 402 (2022), Iss. P.113794
https://doi.org/10.1016/j.cam.2021.113794 [Citations: 3]