Abstract

Reliable and efficient residual-based a posteriori error estimates are established for the nonconforming finite element method for the Reissner--Mindlin plate due to Arnold and Falk [SIAM J. Numer. Anal., 26 (1989), pp. 1276--1290]. The error is estimated by a computable error estimator from above and below up to multiplicative constants that depend neither on the mesh-size nor on the plate's thickness. The error is controlled in norms that are known to converge to zero in a quasi-optimal way.

MSC codes

  1. 65N30
  2. 65R20
  3. 73C50

Keywords

  1. Reissner--Mindlin
  2. plate
  3. a posteriori error estimates
  4. adaptive algorithm
  5. reliability
  6. efficiency
  7. mixed finite element method
  8. nonconforming finite element method

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References

1.
Douglas Arnold, Richard Falk, A uniformly accurate finite element method for the Reissner‐Mindlin plate, SIAM J. Numer. Anal., 26 (1989), 1276–1290
2.
I. Babuška and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15 (1978), pp. 736–754.
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Dietrich Braess, Finite elements, Cambridge University Press, 1997xvi+323, Theory, fast solvers, and applications in solid mechanics; Translated from the 1992 German original by Larry L. Schumaker
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Susanne Brenner, L. Scott, The mathematical theory of finite element methods, Texts in Applied Mathematics, Vol. 15, Springer‐Verlag, 1994xii+294
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Franco Brezzi, Michel Fortin, Mixed and hybrid finite element methods, Springer Series in Computational Mathematics, Vol. 15, Springer‐Verlag, 1991x+350
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C. Carstensen, S. Bartels, and S. Jansche, A Posteriori Error Estimates for Nonconforming Finite Element Methods, report 00‐13 Berichtsreihe des Mathematischen Seminars der Universität Kiel, Kiel, Germany, 2000;
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P. Clément, Approximation by finite element functions using local regularization, RAIRO Sér. Rouge Anal. Numér., R‐2 (1975), pp. 77–84.
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Philippe Ciarlet, The finite element method for elliptic problems, North‐Holland Publishing Co., 1978xix+530, Studies in Mathematics and its Applications, Vol. 4
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E. Dari, R. Duran, C. Padra, V. Vampa, A posteriori error estimators for nonconforming finite element methods, RAIRO Modél. Math. Anal. Numér., 30 (1996), 385–400
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Kenneth Eriksson, Don Estep, Peter Hansbo, Claes Johnson, Introduction to adaptive methods for differential equations, Acta Numer., Cambridge Univ. Press, Cambridge, 1995, 105–158
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Information & Authors

Information

Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 2034 - 2044
ISSN (online): 1095-7170

History

Published online: 26 July 2006

MSC codes

  1. 65N30
  2. 65R20
  3. 73C50

Keywords

  1. Reissner--Mindlin
  2. plate
  3. a posteriori error estimates
  4. adaptive algorithm
  5. reliability
  6. efficiency
  7. mixed finite element method
  8. nonconforming finite element method

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