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Admissible Regions for Higher-Order Finite Volume Method Grids
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AbstractAdmissible 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.
Title: Admissible Regions for Higher-Order Finite Volume Method Grids
Description:
AbstractAdmissible 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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