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Mixed discontinuous Galerkin methods for Darcy flow. (English) Zbl 1103.76031
The authors consider a family of mixed finite element discretizations of Darcy flow equations using totally discontinuous elements (both for the pressure and flux variable). Instead of using a jump stabilization as it is usually done in discontinuous Galerkin methods, they use the stabilization introduced in A. Masud and T. J. R. Hughes [Comput. Methods Appl. Mech. Eng. 191, No. 39–40, 4341–4370 (2002; Zbl 1015.76047)]. They show that such stabilization works for discontinuous elements as well, provided that both the pressure and the flux are approximated by local polynomials of degree greater than 1, without any need for additional jump terms.

MSC:
76M10Finite element methods (fluid mechanics)
76S05Flows in porous media; filtration; seepage
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
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[20]
[21] · Zbl 0384.65058 · doi:10.1137/0715010