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A stabilised finite element method for the plate obstacle problem

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Abstract

We introduce a stabilised finite element formulation for the Kirchhoff plate obstacle problem and derive both a priori and residual-based a posteriori error estimates using conforming \(C^1\)-continuous finite elements. We implement the method as a Nitsche-type scheme and give numerical evidence for its effectiveness in the case of an elastic and a rigid obstacle.

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Authors and Affiliations

  1. VTT Technical Research Centre of Finland Ltd, P.O. Box 1000, 02044 VTT, Espoo, Finland

    Tom Gustafsson

  2. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, 00076, Aalto, Finland

    Rolf Stenberg

  3. CAMGSD/Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Juha Videman

Authors
  1. Tom Gustafsson
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  2. Rolf Stenberg
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  3. Juha Videman
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Corresponding author

Correspondence to Rolf Stenberg.

Additional information

Communicated by Axel Målqvist.

Funding from Tekes (Decision No. 3305/31/2015), the Finnish Cultural Foundation, the Portuguese Science Foundation (FCOMP-01-0124-FEDER-029408) and the Finnish Society of Science and Letters is greatly acknowledged.

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Gustafsson, T., Stenberg, R. & Videman, J. A stabilised finite element method for the plate obstacle problem. Bit Numer Math 59, 97–124 (2019). https://doi.org/10.1007/s10543-018-0728-7

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  • DOI: https://doi.org/10.1007/s10543-018-0728-7

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