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New error estimates of biquadratic Lagrange elements for Poisson's equation

文献类型：期刊论文

作者Huang, HT; Li, ZC; Zhou, AH
刊名APPLIED NUMERICAL MATHEMATICS
出版日期2006-05-01
卷号56期号:5页码:712-744
关键词lagrange elements biquadratic elements Poisson's equation global superconvergence ultraconvergence
ISSN号0168-9274
DOI10.1016/j.apnum.2005.06.003
英文摘要In this paper, we report some new ultraconvergence results of biquadratic Lagrange elements for the Dirichlet problem of Poisson's equation, -Delta u = f. The point-line-area interpolant in [V Girault, P.A. Raviart, A Finite Element Methods for Navier-Stokes Equation, Theory and Algorithms, Springer, 1986] is chosen in this paper, instead of the traditional pure point interpolant in [P.G. Ciarlet, Basic error estimates for elliptic problems, in: P.G. Ciarlet, J.L. Lions (Eds.), Finite Element Methods, Part 1, North-Holland, Amsterdam, 199 1, pp. 17-351]. Suppose that the solution is smooth enough, by means of an a posteriori interpolant, the ultraconvergence O(h(4)) in H I norm is proved for uniform rectangles rectangle(ij), and the higher ultraconvergence O(h(6-l)) in H-l (l = 0, 1) norm under the special case of uniform squares rectangle(ij) and f(xxyy) = 0. Even when f(xxyy) not equal 0, we propose two techniques: (1) the Richardson extrapolation method and (2) the correction method, to retain the same higher ultraconvergence results. Moreover, the ultraconvergence O(h(6-l) vertical bar 1nh vertical bar) is also proved for l (l = 0, 1) order infinite norms. In this paper, the numerical experiments are provided to validate all the ultraconvergence results made. Note that the new ultraconvergence results under the special case are three order higher than the optimal convergence rate in [P.G. Ciarlet, Basic error estimates for elliptic problems, in: P.G. Ciarlet, J.L. Lions (Eds.), Finite Element Methods, Part 1, North-Holland, Amsterdam, 1991, pp. 17=351], and one order than that in [Q. Lin, N. Yan, A. Zhou, A rectangle test for interpolated finite elements, in: Proc. Sys. Sci. and Sys. Engrg., Great Wall Culture Publishers, Hong Kong, 1991, pp. 217-229].
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000236426000008
出版者ELSEVIER SCIENCE BV
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/2644]  
专题计算数学与科学工程计算研究所
通讯作者Li, ZC
作者单位1.Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan
2.Natl Sun Yat Sen Univ, Dept Comp Sci & Engn, Kaohsiung 80424, Taiwan
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式
GB/T 7714		 Huang, HT,Li, ZC,Zhou, AH. New error estimates of biquadratic Lagrange elements for Poisson's equation[J]. APPLIED NUMERICAL MATHEMATICS,2006,56(5):712-744.
APA Huang, HT,Li, ZC,&Zhou, AH.(2006).New error estimates of biquadratic Lagrange elements for Poisson's equation.APPLIED NUMERICAL MATHEMATICS,56(5),712-744.
MLA Huang, HT,et al."New error estimates of biquadratic Lagrange elements for Poisson's equation".APPLIED NUMERICAL MATHEMATICS 56.5(2006):712-744.

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来源：数学与系统科学研究院

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