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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A locking-free Reissner-Mindlin quadrilateral element


Authors: Huo-Yuan Duan and Guo-Ping Liang
Journal: Math. Comp. 73 (2004), 1655-1671
MSC (2000): Primary 65N30
Published electronically: November 24, 2003
MathSciNet review: 2059730
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Abstract: On arbitrary regular quadrilaterals, a new finite element method for the Reissner-Mindlin plate is proposed, where both transverse displacement and rotation are approximated by isoparametric bilinear elements, with local bubbles enriching rotation, and a local reduction operator is applied to the shear energy term. This new method gives optimal error bounds, uniform in the thickness of the plate, for both transverse displacement and rotation with respect to $H^1$and $L^2$ norms.


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Additional Information

Huo-Yuan Duan
Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China
Email: dhymath@yahoo.com.cn, hyduan@lsec.cc.ac.cn

Guo-Ping Liang
Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China
Email: guoping@math03.math.ac.cn, ling@fegensoft.com

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01619-3
PII: S 0025-5718(03)01619-3
Keywords: Reissner-Mindlin plates, finite element method
Received by editor(s): July 19, 2002
Received by editor(s) in revised form: March 17, 2003
Published electronically: November 24, 2003
Article copyright: © Copyright 2003 American Mathematical Society