Mimetic finite difference methods for diffusion equations Academic Article

abstract

• 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.

authors

• Morel, Jim

published proceedings

• COMPUTATIONAL GEOSCIENCES

author list (cited authors)

• Hyman, J., Morel, J., Shashkov, M., & Steinberg, S.

citation count

• 99

complete list of authors

• Hyman, J||Morel, J||Shashkov, M||Steinberg, S

publication date

• September 2002

publisher

• Springer Nature  Publisher

published in

• Computational Geosciences: modeling, simulation and data analysis  Journal

keywords

• Diffusion Equations
• Locally Conservative Method
• Mimetic Discretizations

Digital Object Identifier (DOI)

• 10.1023/A:1021282912658

start page

• 333

end page

• 352

volume

• 6

issue

• 3-4

URL

• http://dx.doi.org/10.1023/a:1021282912658