An Arbitrary Order Mimetic Finite Difference Method for the 3D DeRham Complex

V. Gyrya, G. Manzini, D. A. McGregor (Oregon State University)

Mimetic Finite Difference methods have seen intensive development; however, a large amount of work has been primarily focused on the development of lowest order schemes. The MFD technology offers a large number of advantages namely by working on very general polyhedral meshes (therefore supporting automatic local refinement) and by preserving many properties of vector calculus in a discrete sense. By discretizing the DeRham Complex we can produce discretizations for a large number of PDEs arising in many application areas.

We present some promising preliminary results on the construction of a high order complex which includes spaces analogous to Nedelec and Raviart-Thomas elements on tetrahedral meshes.