Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing

ZHAO Qing-hua; ZHOU Shu-zi; ZHU Qi-ding

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(4): 401-405

ZHAO Qing-hua, ZHOU Shu-zi, ZHU Qi-ding. Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing[J]. Applied Mathematics and Mechanics, 2007, 28(4): 401-405.

Citation:

ZHAO Qing-hua, ZHOU Shu-zi, ZHU Qi-ding. Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing[J]. Applied Mathematics and Mechanics, 2007, 28(4): 401-405.

Citation:

ZHAO Qing-hua, ZHOU Shu-zi, ZHU Qi-ding. Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing[J]. Applied Mathematics and Mechanics, 2007, 28(4): 401-405.

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Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing

1.
College of Mathematics and Economatics, Hunan University, Changsha 410082, P. R. China;

Received Date: 2006-05-31
Rev Recd Date: 2007-02-06
Publish Date: 2007-04-15

Abstract

Abstract

Fora class of two-point boundary value problems, by virtue of one-dimensional projection interpolation and finite element superconvergence fundamental estimations, it was proved that the nodal recovery derivative obtained by Yuan's element energy projection (EEP) method had the optimal order superconvergence on condition that the degree of finite element space is no more than 4. The theoretical analysis coincides with the reported numerical results.
- superconvergence stress,
- element energy projection method,
- finite element,
- two-point boundary value problems,
- projection interpolation

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References(6)

References

[1]	ZHANG Tie.The derivative patch interpolating recovery technique and superconvergence[J].Chinese J Numer Math Appl,2001,(2):1-10.
[2]	ZHU Qi-ding,ZHAO Qing-hua. SPR technique and finite element correction[J].Numer Math,2003，96(4):185-196. doi: 10.1007/s00211-003-0474-9
[3]	CHEN Chuan-miao,XIE Zi-qing,LIU Jing-hong.New error expansion for one dimensional finite element and ultraconvergence[J].Numer Math J Chinese Univ,2005,14(4):296-304.
[4]	袁驷，王玫.一维有限元后处理超收敛解答的EEP法[J].工程力学，2004，21(2):1-9.
[5]	林群，朱起定.有限元预处理与后处理理论[M].上海：上海科学技术出版社，1994.
[6]	Douglas J,Dupont T.Galerkin approximations for the two point boundary problems using continuous,piecewise polynomial spaces[J].Numer Math,1974,22:99-109. doi: 10.1007/BF01436724