Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods

doi:10.1137/040614293

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	Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods
	Fairweather, Graeme ; Lin, Qun ; Lin, Yanping ; Wang, Junping ; Zhang, Shuhua
	2006
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	44 期号:3 页码:1122-1149
摘要	In this paper asymptotic error expansions for mixed finite element approximations of general second order elliptic problems are derived under rectangular meshes, and the Richardson extrapolation is applied to improve the accuracy of the approximations by two different schemes with the help of an interpolation postprocessing technique. The results of this paper provide new asymptotic expansions and new approximate solutions which are one-order and a half-order higher in accuracy than those obtained in [J. Wang, Math Comp., 56 ( 1991), pp. 477 - 503] and [ H. Chen, R. E. Ewing, and R. Lazarov, Asymptotic Error Expansion for the Lowest Order Raviart - Thomas Rectangular Mixed Finite Elements, Technical report ISC-97- 01, 1997], respectively. As a by-product, we illustrate that all the approximations of higher accuracy can be used to form a class of a posteriori error estimators for the mixed finite element method.
关键词	second order elliptic problems mixed finite element methods asymptotic expansions interpolation postprocessing a posteriori error estimators
DOI	10.1137/040614293
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000239038700011
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/3780
专题	中国科学院数学与系统科学研究院
通讯作者	Fairweather, Graeme
作者单位	1.Colorado Sch Mines, Dept Math & Comp Sci, Golden, CO 80401 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 4.Natl Sci Fdn, Div Math Sci, Arlington, VA 22230 USA 5.Univ Finance & Econ, Dept Math, Tianjin 300222, Peoples R China 6.Nankai Univ, Liu Hui Ctr Appl Math, Tianjin 30072, Peoples R China 7.Tianjin Univ, Tianjin 30072, Peoples R China
推荐引用方式 GB/T 7714	Fairweather, Graeme,Lin, Qun,Lin, Yanping,et al. Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2006,44(3):1122-1149.
APA	Fairweather, Graeme,Lin, Qun,Lin, Yanping,Wang, Junping,&Zhang, Shuhua.(2006).Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods.SIAM JOURNAL ON NUMERICAL ANALYSIS,44(3),1122-1149.
MLA	Fairweather, Graeme,et al."Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods".SIAM JOURNAL ON NUMERICAL ANALYSIS 44.3(2006):1122-1149.