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Numerical comparison of robustness of some reduction methods in rough grids. (English) Zbl 1308.76167

Summary: We present three nonsymmetric mixed hybrid \(\text{RT}^{\frac{1}{2}}\) methods and compare with some recently developed reduction methods which are suitable for the single-phase Darcy flow problem with full anisotropic and highly heterogeneous permeability on general quadrilateral grids. The methods reviewed are multipoint flux approximation (MPFA), multipoint flux mixed finite element method, mixed-finite element with broken \(\text{RT}^{\frac{1}{2}}\) method, MPFA-type mimetic finite difference method, and symmetric mixed-hybrid finite element method. The numerical experiments of these methods on different distorted meshes are compared, as well as their differences in performance of fluxes are discussed.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M20 Finite difference 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
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