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Discontinuous Galerkin with Weakly Over-Penalized Techniques for Reissner–Mindlin Plates

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Abstract

In this article we introduce a new locking-free completely discontinuous formulation for Reissner–Mindlin plates that combines the discontinuous Galerkin methods with weakly over-penalized techniques. We establish a new discrete version of Helmholtz decomposition and some important residual estimates. Combining the residual estimates with enriching operators we derive an optimal a priori error estimate in the energy norm. We obtain robust a posteriori error estimators and prove their reliability and efficiency.

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Acknowledgments

This work was developed while the first author was visiting the Department of Mathematics at Humboldt University. He wishes to express his gratitude to this institution for its hospitality.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Santa Catarina, Trindade, Florianópolis, SC, 88040-900, Brazil

    Paulo Rafael Bösing

  2. Institut für Mathematik, Humboldt–Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Carsten Carstensen

Authors
  1. Paulo Rafael Bösing
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  2. Carsten Carstensen
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Corresponding author

Correspondence to Paulo Rafael Bösing.

Additional information

This work was supported by CNPq (National Council for Scientific and Technological Development—Brazil).

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Bösing, P.R., Carstensen, C. Discontinuous Galerkin with Weakly Over-Penalized Techniques for Reissner–Mindlin Plates. J Sci Comput 64, 401–424 (2015). https://doi.org/10.1007/s10915-014-9936-8

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  • DOI: https://doi.org/10.1007/s10915-014-9936-8

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