Paper Info
Title
Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes
Abstract
We developed a new monotone finite volume method for diffusion equations. The second-order linear methods, such as the multipoint flux approximation, mixed finite element and mimetic finite difference methods, are not monotone on strongly anisotropic meshes or for diffusion problems with strongly anisotropic coefficients. The finite volume (FV) method with linear two-point flux approximation is monotone but not even first-order accurate in these cases. The developed monotone method is based on a nonlinear two-point flux approximation. It does not require any interpolation scheme and thus differs from other nonlinear finite volume methods based on a two-point flux approximation. The second-order convergence rate is verified with numerical experiments.
Year
DOI
Venue
2009
10.1016/j.jcp.2008.09.031
J. Comput. Physics
Keywords
Field
DocType
diffusion equation,mixed finite element,multipoint flux approximation,polygonal mesh,finite volume,two-point flux approximation,mimetic finite difference method,nonlinear two-point flux approximation,linear two-point flux approximation,developed monotone method,monotone method,new monotone finite volume,nonlinear finite volume method,interpolation-free monotone finite volume,convergence rate,finite volume method,second order,finite difference method,first order
Mathematical optimization,Regular grid,Mathematical analysis,Extended finite element method,Finite difference coefficient,Finite difference method,Finite volume method,Monotone polygon,Mathematics,Finite volume method for one-dimensional steady state diffusion,Mixed finite element method
Journal
Volume
Issue
ISSN
228
3
Journal of Computational Physics
Citations 
PageRank 
References 
32
1.82
6
Authors
3
Name
Order
Citations
PageRank
K. Lipnikov152157.35
Daniil Svyatskiy217012.13
Yuri V. Vassilevski39114.75