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.
X. Wang, "Approximating Stationary Statistical Properties," Chinese Annals of Mathematics. Series B, vol. 30, no. 6, pp. 831 - 844, Springer, Dec 2009.
The definitive version is available at https://doi.org/10.1007/s11401-009-0178-2
Mathematics and Statistics
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)
Article - Journal
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01 Dec 2009