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

Journal Article · Sat Nov 01 04:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.07.001· OSTI ID:1236930

Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu

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.

• Research Organization: Pacific Northwest National Laboratory (PNNL), Richland, WA (US)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-76RL01830
• OSTI ID: 1236930
• Report Number(s): PNNL-SA-105910; KJ0401000
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 276; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English