Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The num...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational physics 2014-11, Vol.276, p.422-437
Main Authors: Lin, Guang, Liu, Jiangguo, Mu, Lin, Ye, Xiu
Format: Article
Language:English
Subjects:
Anisotropy
Computation
Darcy flow
Finite element method
Galerkin methods
Heterogeneity
Mathematical analysis
Mathematical models
Numerical analysis
Porous media
Weak Galerkin
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.07.001