Computational Geosciences 6: 333–352, 2002. 2002 Kluwer Academic Publishers. Printed in the Netherlands. Mimetic

This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materi-als. These difference operators satisfy the fundamental identities, conservation laws and theo-rems of vector and tensor calculus on nonorthogonal, nonsmooth, structured and unstructured computational grids. We provide explicit approximations for equations in two dimensions with discontinuous anisotropic diffusion tensors. We mention the similarities and differences between the new methods and mixed finite element or hybrid mixed finite element meth-ods