A Multipoint Flux Mixed Finite Element Method

Authors:
Mary F. Wheeler;Ivan Yotov
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2006

Citing 0
Cited 14

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Double-families of quasi-positive Darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids

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Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids

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A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

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A Multipoint Flux Mixed Finite Element Method on Hexahedra

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A nine-point scheme with explicit weights for diffusion equations on distorted meshes

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Quasi M-Matrix Multifamily Continuous Darcy-Flux Approximations with Full Pressure Support on Structured and Unstructured Grids in Three Dimensions

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A fully-coupled upwind discontinuous Galerkin method for incompressible porous media flows: High-order computations of viscous fingering instabilities in complex geometry

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Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems

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Mimetic finite difference method

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Abstract

We develop a mixed finite element method for single phase flow in porous media that reduces to cell-centered finite differences on quadrilateral and simplicial grids and performs well for discontinuous full tensor coefficients. Motivated by the multipoint flux approximation method where subedge fluxes are introduced, we consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method. A special quadrature rule is employed that allows for local velocity elimination and leads to a symmetric and positive definite cell-centered system for the pressures. Theoretical and numerical results indicate second-order convergence for pressures at the cell centers and first-order convergence for subedge fluxes. Second-order convergence for edge fluxes is also observed computationally if the grids are sufficiently regular.