"Discrete theories for elliptic problems in non--divergence form"
Time: 11:00 AM
Location: Hill 525
Abstract: In this talk, two discrete theories for elliptic problems in
non-divergence form are presented. The first, which is applicable to
problems with continuous coefficients and is motivated by the strong
solution concept, is based on discrete Calderon-Zygmund-type estimates.
The second theory relies on discrete Miranda-Talenti estimates for
elliptic problems with discontinuous coefficients satisfying the Cordes
condition. Both theories lead to simple, efficient, and convergent
finite element methods. We provide numerical experiments which confirm
the theoretical results, and we discuss possible extensions to fully
nonlinear second order PDEs.
Friday, March 3rd
Ridgway Scott , University of Chicago
"Electron correlation in van der Waals interactions"
Time: 12:00 PM
Location: Hill 423
Abstract: We examine a technique of Slater and Kirkwood which provides an exact resolution of the asymptotic behavior of the van der Waals attraction between two hydrogens atoms. We modify their technique to make the problem more tractable analytically and more easily solvable by numerical methods. Moreover, we prove rigorously that this approach provides an exact solution for the asymptotic electron correlation. The proof makes use of recent results that utilize the Feshbach-Schur perturbation technique. We provide visual representations of the asymptotic electron correlation (entanglement) based on the use of Laguerre approximations.We also describe an a computational approach using the Feshbach-Schur perturbation and tensor-contraction techniques that make a standard finite difference approach tractable.