PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Chun Liu.

Title:Mimetic finite difference method for PDEs
Seminar:CCMA PDEs and Numerical Methods Seminar Series
Speaker:Konstantin Lipnikov, Theoretical Division, Los Alamos National Laboratory
Abstract:
ABSTRACT. A successful discretization method inherits or mimics fundamental properties of the underlying PDEs such as conservation laws, symmetries, solution positivity and maximum principle. Construction of such a method is made more difficult when the mesh is distorted so that it can conform and adapt to the physical domain and problem solution. The talk is about one such method - the mimetic finite difference (MFD) method. The MFD method is used to solve problems with full tensor coefficients on unstructured polygonal and polyhedral meshes. Polyhedral meshes may include arbitrary elements: tetrahedrons, pyramids, hexahedrons, degenerated and non-convex polyhedrons, generalized polyhedrons, etc. Modeling with polyhedral meshes has a number of advantages that will be addressed in the talk. The MFD method has been applied successfully to several applications including diffusion, electromagnetics, acoustics, and gasdynamics. I present a general framework for building MFD methods, give examples of discretizations of the gradient, divergence and curl operators on polygonal and polyhedral meshes, and review existing theoretical results including convergence estimates, orthogonal decomposition theorems, etc. I'll present in more details the MFD methods for solving a linear diffusion problem. I'll show how the method produces a family of schemes with equivalent properties and establish connections with the mixed finite element, finite volume and multi-point flux approximation methods.

Room Reservation Information

Room Number:MB315
Date:05 / 19 / 2008
Time:03:35pm - 04:25pm