TY - JOUR T1 - Admissible Regions for Higher-Order Finite Volume Method Grids 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.