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Admissible Regions for Higher-Order Finite Volume Method Grids

  • Yuanyuan Zhang (a1) and Zhongying Chen (a2)

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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*Corresponding author. Email addresses: yy0dd@126.com (Y. Zhang), lnsczy@mail.sysu.edu.cn (Z. Chen)

References

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