Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, March 14, 2008 - 05:00

Location:

Gilkey 113

Guest Speaker:

Institution:

Los Alamos National Laboratory

Abstract:

ABSTRACT. The mimetic finite difference (MFD) method mimics important properties of physical and mathematical models. As a result, conservation laws, solution symmetries, and the fundamental identities of the vector and tensor calculus are held for discrete models. The MFD method retains these attractive properties for full tensor coefficients and arbitrary polygonal and polyhedral meshes which may include non-convex and degenerate elements. Modeling with polygonal and polyhedral meshes has a number of advantages. For subsurface flows, such meshes allow to describe accurately small, detailed structures such as tilted layers, pinch-outs, irregular inclusions, etc. The polygonal and polyhedral meshes cover the space more efficiently than simplicial meshes which eventually reduces the number of discrete unknowns without lose of accuracy. The locally refined meshes with hanging nodes are particular examples of polygonal and polyhedral meshes with degenerate elements. Such meshes are used frequently to improve resolution in the regions of interest, such as moving fluid fronts, sharp solution variations, etc. The MFD method works for all these meshes. For a linear diffusion problem, I'll discuss important details of the MFD method. In particular, the MFD method gives a rich family of schemes with equivalent properties. For simplicial meshes, I'll show how the MFD method is related to a finite element method. For polygonal and polyhedral meshes, I'll show how new multi-point flux approximation methods can be derived and analyzed using the MFD framework. I'll also compare the MFD method with the Kuznetsov-Repin finite element method.