Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed

doi:10.4208/cicp.060109.130110a

	Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed
	Tang, Tao 1; Zhou, Tao2
	2010-07-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	8 期号:1 页码:226-248
摘要	For a simple model of a scalar wave equation with a random wave speed, Gottlieb and Xiu [Commun. Comput. Phys., 3 (2008), pp. 505-518] employed the generalized polynomial chaos (gPC) method and demonstrated that when uncertainty causes the change of characteristic directions, the resulting deterministic system of equations is a symmetric hyperbolic system with both positive and negative eigen-values. Consequently, a consistent method of imposing the boundary conditions is proposed and its convergence is established under the assumption that the expansion coefficients decay fast asymptotically. In this work, we investigate stochastic collocation methods for the same type of scalar wave equation with random wave speed. It will be demonstrated that the rate of convergence depends on the regularity of the solutions; and the regularity is determined by the random wave speed and the initial and boundary data. Numerical examples are presented to support the analysis and also to show the sharpness of the assumptions on the relationship between the random wave speed and the initial and boundary data. An accuracy enhancement technique is investigated following the multi-element collocation method proposed by Foo, Wan and Karniadakis [J. Comput. Phys., 227 (2008), pp. 9572-9595].
关键词	Hyperbolic equation stochastic collocation methods convergence analysis
DOI	10.4208/cicp.060109.130110a
语种	英语
资助项目	Hong Kong Research Grant Council CERG ; Hong Kong Baptist University FRG ; Natural Science Foundation of China[G10729101]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000278713500009
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10939
专题	计算数学与科学工程计算研究所
通讯作者	Tang, Tao
作者单位	1.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Tang, Tao,Zhou, Tao. Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2010,8(1):226-248.
APA	Tang, Tao,&Zhou, Tao.(2010).Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,8(1),226-248.
MLA	Tang, Tao,et al."Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 8.1(2010):226-248.