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An Overview of Recent Results on Nitsche’s Method for Contact Problems

  • Franz Chouly
  • Mathieu Fabre
  • Patrick Hild
  • Rabii Mlika
  • Jérôme Pousin
  • Yves Renard
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 121)

Abstract

We summarize recent achievements in applying Nitsche’s method to some contact and friction problems. We recall the setting of Nitsche’s method in the case of unilateral contact with Tresca friction in linear elasticity. Main results of the numerical analysis are detailed: consistency, well-posedness, fully optimal convergence in H1(Ω)-norm, residual-based a posteriori error estimation. Some numerics and some recent extensions to multi-body contact, contact in large transformations and contact in elastodynamics are presented as well.

Notes

Acknowledgements

The authors thank Erik Burman, the editorial board and Springer for the invitation to write this paper for their special volume. Moreover they thank the two anonymous referees for their constructive comments that helped to improve the paper. They thank also Thomas Boiveau and Susanne Claus for the GUFEM meeting and discussions. The first author thanks Région Bourgogne Franche-Comté for partial funding (“Convention Région 2015C-4991. Modèles mathématiques et méthodes numériques pour l’élasticité non-linéaire”), as well as Erik Burman and Miguel A. Fernández for some inspiring discussions on Nitsche’s method.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Franz Chouly
    • 1
  • Mathieu Fabre
    • 2
    • 3
  • Patrick Hild
    • 4
  • Rabii Mlika
    • 5
  • Jérôme Pousin
    • 5
  • Yves Renard
    • 5
  1. 1.Laboratoire de Mathématiques de Besançon - UMR CNRS 6623Université Bourgogne Franche–Comté25030 Besançon CedexFrance
  2. 2.EPFL SB MATHICSE (Bt. MA)LausanneSwitzerland
  3. 3.Istituto di Matematica Applicata e TecnologieInformatiche “E. Magenes” del CNRPaviaItaly
  4. 4.Institut de Mathématiques de Toulouse - UMR CNRS 5219Université Paul SabatierToulouse Cedex 9France
  5. 5.CNRS, INSA-Lyon, ICJ UMR5208Université de LyonF-69621 VilleurbanneFrance

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