A SECOND-ORDER FLUX APPROXIMATION FOR THE MIMETIC FINITE DIFFERENCE APPROXIMATION OF DIFFUSION PROBLEMS L. Beirao da 1 Veiga , K. 2 Lipnikov , G. 3 Manzini Dipartimento di Matematica “G. Enriques”, Università degli Studi di Milano, Italy 2 Los Alamos National Laboratory, Theoretical Division, Los Alamos, New Mexico, US 3 Istituto di Matematica Applicata e Tecnologie Informatiche - CNR, Pavia, Italy 1 INTRODUCTION. The Mimetic Finite Difference (MFD) method is designed to mimic HIGHER-ORDER FLUX APPROXIMATION essential properties of the PDEs and the fundamental identities of the vector and tensor calculus. The MFD method provides a low-order discretization of the diffusion equation in mixed form on general polyhedral meshes. The numerical scheme is second-order accurate for the scalar variable due to a superconvergence effect, but the flux approximation is only first-order accurate. In this work, we present a high-order extension of the MFD scheme, which is second-order accurate for both the scalar and the flux approximation. DESCRIPTION. NUMERICAL RESULTS: a sequence of “randomized” grids, where refined grids are not nested into coarser meshes. THEORETICAL RESULTS: (circles) (squares) P1 local consistency with constant diffusion tensor: Modified P1 local consistency with non-constant diffusion tensor: REFERENCES 1) L. Beirão da Veiga, K. Lipnikov, and G. Manzini. Convergence analysis of the high-order mimetic finite difference method. (2008). To appear in Numerische Mathematik. 2) L. Beirão da Veiga and G. Manzini. A higher-order formulation of the mimetic finite difference method. SIAM, J. Sci. Comput., 31(1):732-760, 2008.