Mimetic finite difference methods for diffusion equations. (English) Zbl 1023.76033

Hyman, J.; Morel, J.; Shashkov, M.; Steinberg, S.

Comput. Geosci. 6, No. 3-4, 333-352 (2002).

Summary: This paper reviews and extends the theory and application of mimetic finite difference methods for the solution of diffusion problems in strongly heterogeneous anisotropic materials. These difference operators satisfy the fundamental identities, conservation laws and theorems 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 methods.

MSC:

76M20	Finite difference methods applied to problems in fluid mechanics
76R50	Diffusion

Keywords:

diffusion equations; locally conservative method; mimetic finite difference methods; strongly heterogeneous anisotropic materials; conservation laws; discontinuous anistropic diffusion tensors