PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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Title:Uniformly dissipative approximations of stationary statistical properties
Seminar:CCMA Luncheon Seminar
Speaker:Xiaoming Wang, FSU
Abstract:
We show that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserves the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess highly desirable properties in terms of approximating stationary statistics properties. In particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous in time dynamical system at vanishing mesh size. The idea is illustrated on the infinite Prandtl number model for convection and semi-discrete in time discretization although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. So far as we know, this is the first result on rigorous validation of numerical schemes for approximating stationary statistical properties. Our result may be also viewed as a Lax type result in the sense that consistency and uniform dissipativity implies the convergence of stationary statistical properties.

Room Reservation Information

Room Number:MB114
Date:08 / 31 / 2007
Time:12:15pm - 01:25pm