### Tuesday, July 14

## MS30

Mimetic Finite-Difference Methods for Partial Differential Equations

2:00 PM-4:00 PM

*Room: Sidney Smith 1069*

Numerical solutions of partial differential equations approximated with finite difference methods that preserve and mimic the fundamental properties of the equations automatically reproduce many of the integral identities, including the conservation laws, of the continuum model for the underlying physical problem. These methods can lead to a deeper understanding of how the underlying physics can be captured by the discrete model.

The speakers will discuss the use of discrete vector analysis to derive new mimetic finite difference methods for the divergence, gradient and curl differential operators and show how these discrete operators automatically satisfy the fundamental theorems of vector and tensor analysis. They will describe how the mimetic approach can used to construct accurate finite difference methods on nonuniform grids for solving diffusion equation, Maxwell's equations with rough coefficients. Special attention will be paid to consistent discretizations of boundary conditions.

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

*Los Alamos National Laboratory*
**2:00 The Approximation of Boundary Conditions for Mimetic Finite Difference Methods**
*James M. Hyman* and Mikhail J. Shashkov, Organizers
**2:30 Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion**
- James M. Hyman and
*Mikhail J. Shashkov*, Organizers
**3:00 Mimetic Finite Differences Methods and Navier--Stokes Equations**
- F. Bertagnolio, LIMSI-CNRS, France; and
*Olivier Daube*, CEMIF, Université d'Evry, France
**3:30 Control-Volume Mixed Finite Element Methods and Efficient Algebraic Solvers**
*Thomas F. Russell*, Rossen R. Parashkevov, and John D. Wilson, University of Colorado, Denver

LMH Created: 3/18/98, MMD Updated: 6/22/98