Galerkin methods based on hermite splines for singular perturbation problems

doi:10.1137/040607411

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	Galerkin methods based on hermite splines for singular perturbation problems
	Liu, ST ; Xu, YS
	2006
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	43 期号:6 页码:2607-2623
摘要	We develop Galerkin methods for solving the singularly perturbed two-point boundary value problem of high-order elliptic differential equations. These methods are based on Hermite splines with knots adapted to the singular behavior of the solution of the problem. We prove an optimal order of uniform convergence for the method with respect to the perturbation parameter. Specifically, we present a sufficient condition on the mesh of grid points that ensures the corresponding approximate solution has the optimal order of uniform convergence in the energy norm. We also construct optimal meshes that satisfy the sufficient condition. Numerical examples are presented to illustrate the method and the corresponding theoretical estimates.
关键词	singular perturbation Galerkin methods Hermite splines grid meshes optimal order of uniform convergence
DOI	10.1137/040607411
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000235426500016
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3759
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, ST
作者单位	1.Syracuse Univ, Dept Math, Syracuse, NY 13244 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Liu, ST,Xu, YS. Galerkin methods based on hermite splines for singular perturbation problems[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2006,43(6):2607-2623.
APA	Liu, ST,&Xu, YS.(2006).Galerkin methods based on hermite splines for singular perturbation problems.SIAM JOURNAL ON NUMERICAL ANALYSIS,43(6),2607-2623.
MLA	Liu, ST,et al."Galerkin methods based on hermite splines for singular perturbation problems".SIAM JOURNAL ON NUMERICAL ANALYSIS 43.6(2006):2607-2623.