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Can Finite-Dimensional Maps Approximate the Dynamics of Infinite-Dimensional Systems?


Speaker: Don A. Jones, Arizona St.
Location: 202 Wellman
Start time: Fri, Sep 29 2000, 4:10PM

The solution operator of many PDEs generates infinite-dimensional dynamical systems. However, numerical algorithms approximating solutions of such PDEs 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.