For more information about this meeting, contact Chun Liu.
| Title: | Mimetic finite difference method for PDEs |
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| Seminar: | CCMA PDEs and Numerical Methods Seminar Series |
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| Speaker: | Konstantin Lipnikov, Theoretical Division, Los Alamos National Laboratory |
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| Abstract: |
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| 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 |
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| Date: | 05 / 19 / 2008 |
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| Time: | 03:35pm - 04:25pm |
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