A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions

doi:10.1093/imanum/drn048

	A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions
	Liu, Fang 2; Madden, Niall 3; Stynes, Martin 1; Zhou, Aihui4
	2009-10-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	29 期号:4 页码:986-1007
摘要	The linear reaction-diffusion problem - epsilon(2)delta u + bu = f is considered on the unit square with homogeneous Dirichlet boundary conditions. Here epsilon is a small positive parameter and the problem is in general singularly perturbed. The numerical solution of this problem is analysed on a Shishkin mesh that has N intervals in each coordinate direction, using the Galerkin finite-element method with bilinear trial functions. The accuracy of this method, measured in the associated energy norm, is shown to be O(N(-2) + epsilon(1/2)N(-1) ln N). It is proved that a two-scale sparse grid method achieves the same order of accuracy while reducing the number of degrees of freedom from O(N(2)) to O(N(3/2)). These results are then generalized to systems of reaction-diffusion equations.
关键词	reaction-diffusion finite element Shishkin mesh two-scale discretization sparse grid
DOI	10.1093/imanum/drn048
语种	英语
资助项目	National Natural Science Foundation of China[10701083] ; National Natural Science Foundation of China[10425105] ; National Basic Research Program of China[2005CB321704] ; National University of Ireland, Cork
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000271379100007
出版者	OXFORD UNIV 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/7831
专题	计算数学与科学工程计算研究所
通讯作者	Stynes, Martin
作者单位	1.Natl Univ Ireland, Dept Math, Cork, Ireland 2.Cent Univ Finance & Econ, Sch Appl Math, Beijing 100081, Peoples R China 3.Natl Univ Ireland, Dept Math, Galway, Ireland 4.Chinese Acad Sci, Engn Comp Acad Math & Syst Sci, Inst Computat Math & Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Fang,Madden, Niall,Stynes, Martin,et al. A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2009,29(4):986-1007.
APA	Liu, Fang,Madden, Niall,Stynes, Martin,&Zhou, Aihui.(2009).A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions.IMA JOURNAL OF NUMERICAL ANALYSIS,29(4),986-1007.
MLA	Liu, Fang,et al."A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions".IMA JOURNAL OF NUMERICAL ANALYSIS 29.4(2009):986-1007.