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An optimal adaptive finite element method for elastoplasticity

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Abstract

An adaptive finite element algorithm for problems in elastoplasticity with hardening is proven to be of optimal convergence with respect to the notion of approximation classes. The results rely on the equivalence of the errors of the stresses and energies resulting from Jensen’s inequality. Numerical experiments study the influence of the hardening and bulk parameters to the convergence behavior of the AFEM algorithm. This is the first optimal adaptive FEM for a variational inequality.

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Authors and Affiliations

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

    Carsten Carstensen & Sebastian Wiedemann

  2. Department of Computational Science and Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, 120-749, Korea

    Carsten Carstensen

  3. Department of Mathematics, University of Salzburg, Hellbrunnerstraße 34, 5020, Salzburg, Austria

    Andreas Schröder

Authors
  1. Carsten Carstensen
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  2. Andreas Schröder
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  3. Sebastian Wiedemann
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Corresponding author

Correspondence to Andreas Schröder.

Additional information

This work was supported by the DFG Research Center Matheon, Project C13.

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Carstensen, C., Schröder, A. & Wiedemann, S. An optimal adaptive finite element method for elastoplasticity. Numer. Math. 132, 131–154 (2016). https://doi.org/10.1007/s00211-015-0714-9

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  • DOI: https://doi.org/10.1007/s00211-015-0714-9

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