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Volume 7, Issue 2
Admissible Regions for Higher-Order Finite Volume Method Grids

Yuanyuan Zhang & Zhongying Chen

DOI: 10.4208/eajam.290416.161016a

East Asian J. Appl. Math., 7 (2017), pp. 269-285.

Published online: 2018-02

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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 method, admissible region, uniform local-ellipticity.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-269, author = {Yuanyuan Zhang and Zhongying Chen}, title = {Admissible Regions for Higher-Order Finite Volume Method Grids}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.290416.161016a}, url = {http://global-sci.org/intro/article_detail/eajam/10749.html} }
TY - JOUR T1 - Admissible Regions for Higher-Order Finite Volume Method Grids AU - Yuanyuan Zhang & Zhongying Chen JO - East Asian Journal on Applied Mathematics VL - 2 SP - 269 EP - 285 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.290416.161016a UR - https://global-sci.org/intro/article_detail/eajam/10749.html KW - Finite volume method, admissible region, uniform local-ellipticity. AB -

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.

Yuanyuan Zhang and Zhongying Chen. (2018). Admissible Regions for Higher-Order Finite Volume Method Grids. East Asian Journal on Applied Mathematics. 7 (2). 269-285. doi:10.4208/eajam.290416.161016a
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