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 | |
刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
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2006 | |
卷号 | 44期号:3页码:1122-1149 |
关键词 | second order elliptic problems mixed finite element methods asymptotic expansions interpolation postprocessing a posteriori error estimators |
ISSN号 | 0036-1429 |
DOI | 10.1137/040614293 |
英文摘要 | 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. |
WOS研究方向 | Mathematics |
语种 | 英语 |
出版者 | SIAM PUBLICATIONS |
WOS记录号 | WOS:000239038700011 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3779] ![]() |
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. |
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