UTA Department of Mathematics

Special Mathematics Colloquium

Date/Time/Room: Friday (5/10/2002) at 2:00pm in 487 Pickard Hall

Speaker: Don A. Jones, Department of Mathematics and Statistics, Arizona State University

``Can Finite-Dimensional Maps Capture the Dynamics of Infinite-Dimensional Systems?''

Abstract: The solution operator of PDEs generates infinite-dimensional dynamical systems. However, numerical algorithms approximating the solutions are inherently finite dimensional. Work suggesting numerical schemes can capture the correct dynamics of the infinite-dimensional systems they approximate, provided the space and time mesh are sufficiently refined, will be presented. The theory is applied to the Navier-Stokes equations, and estimates on the resolution required of the numerical scheme are also given.