Title:         A multipoint flux mixed finite element method

Authors:       M. F. Wheeler and I. Yotov

Source:        SIAM J. Numer. Anal. vol 44, No 5 (2006) 2082-2106

Status:        Published

Abstarct: 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 sub-edge 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 sub-edge
fluxes. Second-order convergence for edge fluxes is also observed
computationally if the grids are sufficiently regular.