CONVERGENCE OF THE MULTIPOINT FLUX APPROXIMATION L-METHOD ON GENERAL GRIDS.

We prove first order convergence of the flux and the pressure for the multipoint flux approximation (MPFA) method known as the MPFA L-method. The proof is based on that presented for the mimetic finite difference paper by Brezzi, Lipnikov, and Shashkov in 2005. Particular to this procedure is that no velocity interpolation is needed inside the element. Hence the volume integration of the velocity field is substituted with a quadrature involving only the fluxes. The proof is valid on polyhedra but limits the possibility of the MPFA L-method to choose a stencil to each and every half-face, as is the usual procedure. The assumption needed for convergence is local and poses limits on grid deformation and the anisotropy of the permeability tensor. This assumption is then used to compare the convergence properties of the MPFA L-method with those of the MPFA O-method and the mimetic finite difference method. [ABSTRACT FROM AUTHOR]