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A posteriori error analysis for conforming MITC elements for Reissner-Mindlin plates


Authors: C. Carstensen and Jun Hu
Journal: Math. Comp. 77 (2008), 611-632
MSC (2000): Primary 65N30, 65N15, 35J25
DOI: https://doi.org/10.1090/S0025-5718-07-02028-5
Published electronically: October 18, 2007
MathSciNet review: 2373172
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Abstract: This paper establishes a unified a posteriori error estimator for a large class of conforming finite element methods for the Reissner-Mindlin plate problem. The analysis is based on some assumption (H) on the consistency of the reduction integration to avoid shear locking. The reliable and efficient a posteriori error estimator is robust in the sense that the reliability and efficiency constants are independent of the plate thickness $ t$. The presented analysis applies to all conforming MITC elements and all conforming finite element methods without reduced integration from the literature.


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Additional Information

C. Carstensen
Affiliation: Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany
Email: cc@math.hu-berlin.de

Jun Hu
Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: hujun@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-07-02028-5
Keywords: A posteriori, error analysis, Reissner-Mindlin Plate, MITC element
Received by editor(s): March 3, 2006
Received by editor(s) in revised form: November 11, 2006
Published electronically: October 18, 2007
Additional Notes: The first author was supported by DFG Research Center MATHEON “Mathematics for key technologies” in Berlin
The second author was partially supported by Natural Science Foundation of China under Grant 10601003 A Foundation for the Author of Excellent Doctoral Dissertation of PR China 200718
Article copyright: © Copyright 2007 American Mathematical Society