THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS

	THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS
	Franz, Sebastian 1; Liu, Fang 2; Roos, Hans-Goerg 1; Stynes, Martin 3; Zhou, Aihui4
	2009-06-01
发表期刊	APPLICATIONS OF MATHEMATICS
ISSN	0862-7940
卷号	54 期号:3 页码:203-223
摘要	Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing N for the maximum number of mesh intervals in each coordinate direction, our "combination" method simply adds or subtracts solutions that have been computed by the Galerkin FEM on N x root N, root N x N and root N x root N meshes. It is shown that the combination FEM yields (up to a factor lnN) the same order of accuracy in the associated energy norm as the Galerkin FEM on an N x N mesh, but it requires only O(N(3/2)) degrees of freedom compared with the O(N(2)) used by the Galerkin FEM. An analogous result is also proved for the streamline diffusion finite element method.
关键词	convection-diffusion finite element Shishkin mesh two-scale discretization
语种	英语
资助项目	National Natural Science Foundation of China[10701083] ; National Natural Science Foundation of China[10425105] ; Chinese National Basic Research Program[2005CB321704] ; National University of Ireland Cork
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000266945200003
出版者	ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8254
专题	计算数学与科学工程计算研究所
通讯作者	Franz, Sebastian
作者单位	1.Tech Univ Dresden, Inst Numer Math, Dresden, Germany 2.Cent Univ Finance & Econ, Beijing, Peoples R China 3.Natl Univ Ireland, Cork, Ireland 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Franz, Sebastian,Liu, Fang,Roos, Hans-Goerg,et al. THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS[J]. APPLICATIONS OF MATHEMATICS,2009,54(3):203-223.
APA	Franz, Sebastian,Liu, Fang,Roos, Hans-Goerg,Stynes, Martin,&Zhou, Aihui.(2009).THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS.APPLICATIONS OF MATHEMATICS,54(3),203-223.
MLA	Franz, Sebastian,et al."THE COMBINATION TECHNIQUE FOR A TWO-DIMENSIONAL CONVECTION-DIFFUSION PROBLEM WITH EXPONENTIAL LAYERS".APPLICATIONS OF MATHEMATICS 54.3(2009):203-223.