DR. STANLY STEINBERG
Department of Mathematics and Statistics
University of New Mexico
Albuquerque, New Mexico
stanly@math.unm.edu

This course is based on my recent research on discretizations continuum mechanics. The topics are:

1. Discretizations in one dimensions -- a discrete calculus with application.
2. Discretizations in three dimensional rectangular grids -- there really are mimetic discretizations.
3. Discretizations in logically-rectangular grids in two dimensions -- they work in complex geometry.
4. Using Mathematica to derive and analyze mimetic discretizations.
5. Convergence of mimetic discretizations.
6. Research problems.

For more information on mimetic discretizations, see Mimetic Discretizations

For background material, see my papers:

· 2003 (Preprint), A Discrete Vector Calculus in Tensor Grids (with Nicolas Robidoux) (ps) (pdf) (Notebook1)
· 2002, A Discrete Calculus with Applications to High-Order Discretizations of Boundary-Value Problems (ps) (pdf) (Notebook1) (Notebook2) (fortran)
· 2002, The Convergence of Mimetic Discretizations for Rough Grids (with M. Hyman) (ps) (pdf)

This course is give at the beginning graduate level, but is accessible to advanced undergraduates with some experience in numerical methods. The required background is vector calculus. Experience with numerical methods for partial differential equations, particularly finite-difference methods will be very helpful.