Abstract

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. the main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. the result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed. © Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2009.

Department(s)

Mathematics and Statistics

Comments

National Science Foundation, Grant None

Keywords and Phrases

Barotropic Quasi-Geostrophic Equations; Dissipative System; Global Attractor; Infinite Prandtl Number Model for Convection; Invariant Measure; Spatial Discretisation; Stationary Statistical Property; Time Discretization; Uniformly Dissipative Scheme

International Standard Serial Number (ISSN)

1860-6261; 0252-9599

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Springer, All rights reserved.

Publication Date

01 Dec 2009

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