Admissible Regions for Higher-Order Finite Volume Method Grids

2017 ◽  
Vol 7 (2) ◽  
pp. 269-285
Author(s):  
Yuanyuan Zhang ◽  
Zhongying Chen
Keyword(s):  
Boundary Value Problems ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Elliptic Boundary ◽  
Higher Order ◽  
Elliptic Boundary Value Problems ◽  
Sufficient Condition ◽  
Elliptic Boundary Value ◽  
Admissible Region ◽  
Volume Method

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.

scholarly journals Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guangcun Lu
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Bifurcation Theory ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Higher Order ◽  
Elliptic Boundary Value Problems ◽  
Elliptic Boundary Value ◽  
Potential Operators ◽  
Linear Elliptic Boundary

<p style='text-indent:20px;'>This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear elliptic boundary value problems of higher order.</p>

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