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 - <p style="text-align: justify;">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.</p>