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Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method

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Abstract

Reliable and efficient residual-based a posteriori error estimates are established for the stabilised locking-free finite element methods for the Reissner-Mindlin plate model. The error is estimated by a computable error estimator from above and below up to multiplicative constants that do neither depend on the mesh-size nor on the plate's thickness and are uniform for a wide range of stabilisation parameter. The error is controlled in norms that are known to converge to zero in a quasi-optimal way. An adaptive algorithm is suggested and run for improving the convergence rates in three numerical examples for thicknesses 0.1, .001 and .001.

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Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Carsten Carstensen

  2. SFB F013 Numerical and Symbolic Scientific Computing, Johannes Kepler University Linz, Freistädterstrasse 313, 4020, Linz, Austria

    Joachim Schöberl

Authors
  1. Carsten Carstensen
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  2. Joachim Schöberl
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Correspondence to Carsten Carstensen.

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Supported by the DFG Research Center MATHEON ``Mathematics for key technologies'' in Berlin and by the Austrian Science Fund Fonds zur Förderung der wissenschaftlichen Forschung, Spezialforschungsbereich F013.

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Carstensen, C., Schöberl, J. Residual-based a posteriori error estimate for a mixed Reißner-Mindlin plate finite element method. Numer. Math. 103, 225–250 (2006). https://doi.org/10.1007/s00211-005-0669-3

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  • DOI: https://doi.org/10.1007/s00211-005-0669-3

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