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Weakly over-penalized discontinuous Galerkin schemes for Reissner–Mindlin plates without the shear variable

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Abstract

This paper introduces a new locking–free formulation that combines the discontinuous Galerkin methods with weakly over-penalized techniques for Reissner–Mindlin plates. We derive optimal a priori error estimates in both the energy norm and \(L^2\) norm for polynomials of degree \(k=2\), and we extend the results concerning the energy norm to higher-order polynomial degrees. Numerical tests confirm our theoretical predictions.

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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. Weakly over-penalized discontinuous Galerkin schemes for Reissner–Mindlin plates without the shear variable. Numer. Math. 130, 395–423 (2015). https://doi.org/10.1007/s00211-014-0672-7

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  • DOI: https://doi.org/10.1007/s00211-014-0672-7

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