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A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics

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Abstract

In this work we consider a stabilized Lagrange (or Kuhn–Tucker) multiplier method in order to approximate the unilateral contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed in the convergence analysis. We propose three approximations of the contact conditions well adapted to this method and we study the convergence of the discrete solutions. Several numerical examples in two and three space dimensions illustrate the theoretical results and show the capabilities of the method.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030, Besançon Cedex, France

    Patrick Hild

  2. Université de Lyon, CNRS, INSA-Lyon, ICJ UMR 5208, LaMCoS UMR 5259, 69621, Villeurbanne, France

    Yves Renard

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  1. Patrick Hild
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Hild, P., Renard, Y. A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer. Math. 115, 101–129 (2010). https://doi.org/10.1007/s00211-009-0273-z

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  • DOI: https://doi.org/10.1007/s00211-009-0273-z

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