Error analysis

The problem of designing control laws to achieve regulation of complex linear or nonlinear systems is a difficult task and has received considerable attention in the engineering literature. This is particularly true in the case of nonlinear systems governed by partial differential equations and especially for the boundary control case where the sensors and actuators produce unbounded operators in the Hilbert state space.

We will give an overview of a residual-type a posteriori error estimation techniques applied to finite element approximations of Hodge-Laplace problems within the finite element exterior calculus (FEEC) framework. Special attention will be given to harmonic forms, their adaptive approximation, and how the quality of their approximation affects the overall error in approximating solutions to the Hodge-Laplace problem. This is joint work with Anil Hirani.

In this talk we present computational techniques for approximation of
Lyapunov exponents based upon smooth matrix factorizations and some
potential applications of these techniques to earth system processes.
Lyapunov exponents characterize stability properties of time dependent
solutions to differential equations. We introduce methods for approximation
of Lyapunov exponents, review results on the sensitivity of Lyapuonv exponents
to perturbations, describe codes we have developed for their computation, and