Date:
Thursday, February 17 Time:
4:00 p.m. Location:
215 Thomas Building Name:
Roland Glowinski Affiliation:
University of Houston Title:
Numerical Methods for some Fully Nonlinear Elliptic Equations

Abstract:glowinski-abstract
This is a joint work with E. J. Dean.
The main goal of this presentation is to discuss the numerical solution of fully
nonlinear elliptic equations (in the sense of Caffarelli-Cabré), a
prototypical one being the celebrated Monge-Ampère equation

completed by boundary conditions (such as Dirichlet's). In (MA-E),
denotes the Hessian of the unknown function .
In order to solve (MA-E), and related equations, we advocate augmented
Lagrangian and (nonlinear) least squares methods which, combined with mixed
finite element approximations and preconditioned conjugate gradient algorithms,
reduce the solution of the above problems to the solution of a sequence of
Poisson problems and of small dimension nonlinear problems (one per grid point,
typically). The results of numerical experiments will be presented; they
concern, among other problems, the solution of (MA-E) and of the following
Pucci's equation

where, in (P-E),
and
(resp.,)
is the largest (resp., the smallest) eigenvalue of .