Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations

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	Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations
	Qu, Dong ; Xu, Chuanju ; Xu CJ(许传炬)
刊名	http://dx.doi.org/10.1016/j.compfluid.2012.10.001
	2013-01
关键词	Stochastic Stokes equations Generalized polynomial chaos Spectral methods Error estimate
英文摘要	In this paper we propose and analyze a high order numerical method to solve the Stokes equations with random coefficients. A stochastic Galerkin approach, based on a finite dimensional Karhunen-Loeve decomposition technique for the stochastic inputs, is used to reduce the original stochastic Stokes equations into a set of deterministic equations for the expansion coefficients. Then a P-N x PN-2 spectral method, together with a block Jacobi iteration is applied to solve the resulting problem. We establish the well-posedness of the weak formulation and its discrete counterpart. Moreover, we provide a rigorous convergence analysis and demonstrate exponential convergence with respect to the degrees of the polynomials chaos expansion used for the approximation in the random direction. Finally, a series of numerical tests is presented to support the theoretical results. (c) 2012 Elsevier Ltd. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66566]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Qu, Dong,Xu, Chuanju,Xu CJ. Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations[J]. http://dx.doi.org/10.1016/j.compfluid.2012.10.001,2013.
APA	Qu, Dong,Xu, Chuanju,&许传炬.(2013).Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations.http://dx.doi.org/10.1016/j.compfluid.2012.10.001.
MLA	Qu, Dong,et al."Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations".http://dx.doi.org/10.1016/j.compfluid.2012.10.001 (2013).