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Space adaptive finite element methods for dynamic Signorini problems

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Abstract

Space adaptive techniques for dynamic Signorini problems are discussed. For discretisation, the Newmark method in time and low order finite elements in space are used. For the global discretisation error in space, an a posteriori error estimate is derived on the basis of the semi-discrete problem in mixed form. This approach relies on an auxiliary problem, which takes the form of a variational equation. An adaptive method based on the estimate is applied to improve the finite element approximation. Numerical results illustrate the performance of the presented method.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Technische Universität Dortmund, 44221, Dortmund, Germany

    Heribert Blum & Andreas Rademacher

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

    Andreas Schröder

Authors
  1. Heribert Blum
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  2. Andreas Rademacher
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  3. Andreas Schröder
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Correspondence to Andreas Rademacher.

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Blum, H., Rademacher, A. & Schröder, A. Space adaptive finite element methods for dynamic Signorini problems. Comput Mech 44, 481–491 (2009). https://doi.org/10.1007/s00466-009-0385-4

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