Adaptive wavelet methods for elliptic operator equations with nonlinear terms

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	Adaptive wavelet methods for elliptic operator equations with nonlinear terms
	Xu, YS ; Zou, QS
	2003-07-01
发表期刊	ADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN	1019-7168
卷号	19 期号:1-3 页码:99-146
摘要	We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategies of both continuous and discrete versions are proposed. We prove that these adaptive methods generate approximate solutions with optimal order in both of convergence and computational complexity when the solutions have certain degree of Besov regularity.
关键词	adaptive wavelet methods tree approximation constructive greedy schemes
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000181690000006
出版者	KLUWER ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18482
专题	中国科学院数学与系统科学研究院
作者单位	1.W Virginia Univ, Dept Math, Morgantown, WV 26506 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xu, YS,Zou, QS. Adaptive wavelet methods for elliptic operator equations with nonlinear terms[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2003,19(1-3):99-146.
APA	Xu, YS,&Zou, QS.(2003).Adaptive wavelet methods for elliptic operator equations with nonlinear terms.ADVANCES IN COMPUTATIONAL MATHEMATICS,19(1-3),99-146.
MLA	Xu, YS,et al."Adaptive wavelet methods for elliptic operator equations with nonlinear terms".ADVANCES IN COMPUTATIONAL MATHEMATICS 19.1-3(2003):99-146.