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

Abstract

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.

Authors:
ORCiD logo; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1236930
Report Number(s):
PNNL-SA-105910
Journal ID: ISSN 0021-9991; KJ0401000
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 276; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Lin, Guang, Liu, Jiangguo, Mu, Lin, and Ye, Xiu. Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity. United States: N. p., 2014. Web. doi:10.1016/j.jcp.2014.07.001.
Lin, Guang, Liu, Jiangguo, Mu, Lin, & Ye, Xiu. Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity. United States. https://doi.org/10.1016/j.jcp.2014.07.001
Lin, Guang, Liu, Jiangguo, Mu, Lin, and Ye, Xiu. 2014. "Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity". United States. https://doi.org/10.1016/j.jcp.2014.07.001.
@article{osti_1236930,
title = {Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity},
author = {Lin, Guang and Liu, Jiangguo and Mu, Lin and Ye, Xiu},
abstractNote = {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.},
doi = {10.1016/j.jcp.2014.07.001},
url = {https://www.osti.gov/biblio/1236930}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 276,
place = {United States},
year = {Sat Nov 01 00:00:00 EDT 2014},
month = {Sat Nov 01 00:00:00 EDT 2014}
}