Monday, July 22

3:15-5:15 PM
## MS8

Mimetic Finite-Difference Methods on Non-Uniform Grids (Part I of II)

A new class of finite difference methods have been derived that preserve and mimic many of the fundamental properties of the divergence, gradient and curl differential operators. Numerical solutions of partial differential equations approximated with these mimetic difference methods, reproduce many of the integral identities, including the conservation laws, of the continuum model for the underlying physical problem.
The derivation of mimetic finite difference methods is based on clear mathematical principals corresponding to basic physical laws. This approach leads to deeper understanding of how the underlying physics, used to derive the equations, can be captured by the discrete model and lead to accurate, robust and stable approximations.

The speakers will describe how the mimetic approach is used to construct accurate difference methods on nonuniform grids for solving elliptic and parabolic equations with rough coefficients, how to construct conservative finite difference methods for Lagrangian gas dynamics, and will compare the accuracy and stability of these new methods with other more commonly used approaches.

**Organizers: James M. Hyman and Mikhail J. Shashkov, **

Los Alamos National Laboratory

**3:15 High-Order Mapping Methods on Nonuniform Grids**
- James M. Hyman and Mikhail J. Shashkov, Organizers
**3:45 A New Numerical Method for Solving Diffusion Equations with Rough Coefficients**
- James M. Hyman and Mikhail J. Shashkov, Organizers; and Stanly Steinberg, University of New Mexico
**4:15 Summation by Parts, Projections, and Stability**
- Pelle Olsson, Stanford University
**4:45 Compatible Discrete Models of Lagrangian Gas Dynamics Method **
- Edward J. Caramana, Los Alamos National Laboratory

*MMD, 5/20/96*