Paper Info
Title
A high-order mimetic method on unstructured polyhedral meshes for the diffusion equation.
Abstract
We present a new family of mimetic finite difference schemes for solving elliptic partial differential equations in the primal form on unstructured polyhedral meshes. These mimetic discretizations are built to satisfy local consistency and stability conditions. The consistency condition is an exactness property, i.e., the mimetic schemes are exact when the solution is a polynomial of an assigned degree. The stability condition ensures the well-posedness of the method. The degrees of freedom are the solution moments on mesh faces and inside mesh cells. Higher order schemes are built using higher order moments. The developed schemes are verified numerically on diffusion problems with constant and spatially variable (possibly, discontinuous) tensorial coefficients.
Year
DOI
Venue
2014
10.1016/j.jcp.2014.04.021
Journal of Computational Physics
Keywords
Field
DocType
High-order method,Unstructured polyhedral mesh,Mimetic finite difference method,Diffusion problem
Local consistency,Higher order moments,Mathematical optimization,Polygon mesh,Polynomial,Mathematical analysis,Finite difference,Stability conditions,Elliptic partial differential equation,Diffusion equation,Mathematics
Journal
Volume
ISSN
Citations 
272
0021-9991
2
PageRank 
References 
Authors
0.42
16
2
Name
Order
Citations
PageRank
K. Lipnikov152157.35
Gianmarco Manzini223927.46