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Mathematics of Computation

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A finite element method for Reissner-Mindlin plates

Author: Huoyuan Duan
Journal: Math. Comp. 83 (2014), 701-733
MSC (2010): Primary 65N30
Published electronically: October 2, 2013
MathSciNet review: 3143689
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Abstract: A finite element method is proposed and analyzed for the Reissner-Mindlin plate problem subject to various boundary conditions. Rotation and transverse displacement variables are approximated by continuous linear elements (enriched with local bubbles) and an $L^2$ projector is applied to the shear energy term onto the Raviart-Thomas $H(\mathrm {div};\Omega )$ finite element. Stability and optimal error bounds hold uniformly in the plate thickness.

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Additional Information

Huoyuan Duan
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, China

Keywords: Reissner-Mindlin plates, finite element method, Raviart-Thomas $H(\textrm {div};\Omega )$ element, Inf-Sup condition
Received by editor(s): August 1, 2010
Received by editor(s) in revised form: June 4, 2011, and January 1, 2012
Published electronically: October 2, 2013
Additional Notes: The author was supported in part by the National Natural Science Foundation of China under grants 11071132 and 11171168 and the Research Fund for the Doctoral Program of Higher Education of China under grant 20100031110002 and 20120031110026.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.