Approximating Stationary Statistical Properties

被引：0

作者：

Xiaoming WANG Department of Mathematics

机构：

来源：

Chinese Annals of Mathematics,Series B | 2009年 / 06期

基金：

美国国家科学基金会;

关键词：

Stationary statistical property; Invariant measure; Global attractor; Dissipative system; Time discretization; Spatial discretisation; Uniformly dissipative scheme; Infinite Prandtl number model for convection; Barotropic quasi-geostrophic equations;

D O I：

暂无

中图分类号：

O415.5 [混沌理论];

学科分类号：

070201 ;

摘要：

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.

引用

页码：831 / 844

页数：14

共 14 条

[1]

Approximation of stationary statistical properties of dissipative dynamical systems: Time discretization[J] . Xiaoming Wang.Mathematics of Computation . 2009 (269)

[2]

Chapter 17 Global attractors in partial differential equations[J] . G. Raugel.Handbook of Dynamical Systems . 2002

[3]

Infinite Prandtl Number Convection[J] . Peter Constantin,Charles R. Doering.Journal of Statistical Physics . 1999 (1)

[4]

Long time stability and convergence for fully discrete nonlinear galerkin methods[J] . Jie Shen.Applicable Analysis . 1990 (4)

[5]

Finite Element Approximation of the Nonstationary Navier-Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time[J] . John G. Heywood,Rolf Rannacher.SIAM Journal on Numerical Analysis . 1986 (4)

[6] THE LONG-TIME BEHAVIOR OF FINITE-ELEMENT APPROXIMATIONS OF SOLUTIONS TO SEMILINEAR PARABOLIC PROBLEMS [J].

LARSSON, S .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1989, 26 (02) :348-365

[7] ON THE CONVERGENCE OF A TIME DISCRETIZATION SCHEME FOR THE NAVIER-STOKES EQUATIONS [J].

GEVECI, T .

MATHEMATICS OF COMPUTATION, 1989, 53 (187) :43-53

[8] Persistence of invariant sets for dissipative evolution equations [J].

Jones, DA ;

Stuart, AM ;

Titi, ES .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 219 (02) :479-502

[9] A uniformly dissipative scheme for stationary statistical properties of the infinite Prandtl number model [J].

Cheng, Wenfang ;

Wang, Xiaoming .

APPLIED MATHEMATICS LETTERS, 2008, 21 (12) :1281-1285

[10] On the long-time stability of the implicit Euler scheme for the two-dimensional Navier-Stokes equations [J].

Tone, F ;

Wirosoetisno, D .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (01) :29-40

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