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Finite Elements for Signorini

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Finite Element Approximation of Contact and Friction in Elasticity

Part of the book series: Advances in Mechanics and Mathematics ((ACM,volume 48))

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Abstract

This chapter is devoted to the finite element approximation of the Signorini problem (3.12) described in previous Chap. 3. We start with the simplest possible setting just to point out the main difficulty that appears in the convergence analysis of many methods. We then present discretizations based on a direct approximation of the variational inequality (3.12), with different alternatives to build discrete convex cones that approximate K. After this, we focus on the derivation of optimal a priori error estimates in the natural H 1-norm related to the approximate solution.

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Authors and Affiliations

  1. University of Burgundy, Dijon, France

    Franz Chouly

  2. Paul Sabatier University, Toulouse, France

    Patrick Hild

  3. National Institute of Applied Sciences of Lyon, Lyon, France

    Yves Renard

Authors
  1. Franz Chouly
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  2. Patrick Hild
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  3. Yves Renard
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Chouly, F., Hild, P., Renard, Y. (2023). Finite Elements for Signorini. In: Finite Element Approximation of Contact and Friction in Elasticity. Advances in Mechanics and Mathematics(), vol 48. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-31423-0_5

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