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Multigrid methods for the biharmonic equation using some nonconforming plate elements

Published online by Cambridge University Press:  17 February 2009


Liming Ma
Affiliation:
Graduate School, Academia Sinica, Beijing 100039, China.
Qianshun Chang
Affiliation:
Academy of Mathematics and Systems Sciences, The Chinese Academy of Sciences, Beijing 100080, China; e-mail: qschang@public.fhnet.cn.net.
Corresponding

Abstract

In this paper, multigrid methods for solving the biharmonic equation using some nonconforming plate elements are considered. An average algorithm is applied to define the transfer operator. A general analysis of convergence is given.


Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Blum, H. and Rannacher, R., “On the boundary value problem of the biharmonic operator on domains with angular corners”, Math. Meth. Appl. Sci. 2 (1980) 556581.CrossRefGoogle Scholar
[2]Braess, D. and Verfurth, R., “Multigrid methods for nonconforming finite element methods”, SIAM J. Numer. Anal. 27 (1990) 979986.CrossRefGoogle Scholar
[3]Bramble, J., Pasciak, J. and Xu, J., “The analysis of multigrid algorithms with nonnested spaces or non-inherited quadratic forms”, Math. Comp. 56 (1991) 134.CrossRefGoogle Scholar
[4]Brenner, S. C., “An optimal-order nonconforming multigrid method for the biharmonic equation”, SIAM J. Numer. Anal. 26 (1989) 11241138.CrossRefGoogle Scholar
[5]Cai, Zhi-Qing, Golastein, C. I. and Pasciak, J. E., “Multilevel iteration for mixed finite element systems with penalty”, SIAM J. Sci. Comput. 14 (1993) 10721088.CrossRefGoogle Scholar
[6]Chang, Qian-Shun and Xu, Lin-Bao, “A numerical method for a system of generalized nonlinear Schrödinger equations”, J. Compur. Math. 4 (1986) 191199.Google Scholar
[7]Ciarlet, P. G., The finite element method for elliptic problem (North-Holland, Amsterdam, 1978).Google Scholar
[8]Golastein, C. I., “Multigrid methods for elliptic problems in unbounded domains”, SIAM J. Numer. Anal. 30 (1993) 159183.CrossRefGoogle Scholar
[9]Lascaux, P. and Lesaint, P., “Some nonconforming finite elements for the plate bending problem”, RAIRO. Anal Numer. 9 (1975) 953.Google Scholar
[10]Shi, Zhong-Ci, “Construction and analysis of a new energy-orthogonal unconventional plate element”, J. Comput. Math. 8 (1990) 7591.Google Scholar
[11]Zhou, Shu-Zi and Gang, Feng, “A multigrid method for the Zienkiewicz element approximation of harmonic equations”. J. Hunan Unv. XueBao 20 (1993) 16.Google Scholar

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