Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity. (English) Zbl 1349.76234 J. Comput. Phys. 276, 422-437 (2014). 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. Cited in 1 ReviewCited in 47 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76S05 Flows in porous media; filtration; seepage Keywords:anisotropy; Darcy flow; heterogeneity; porous media; weak Galerkin Software:iFEM; mfem PDFBibTeX XMLCite \textit{G. Lin} et al., J. Comput. Phys. 276, 422--437 (2014; Zbl 1349.76234) Full Text: DOI References: [1] Arnold, D. N.; Brezzi, F., Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, Modél. Math. Anal. Numér., 19, 7-32 (1985) · Zbl 0567.65078 [2] Arnold, D. N.; Brezzi, F.; Cockburn, B.; Marini, L. D., Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. 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