An overview of recent results on Nitsche's method for contact problems

Franz Chouly (1) , Mathieu Fabre (2, 3) , Patrick Hild (4) , Rabii Mlika (5) , Jerome Pousin (5) , Yves Renard (5)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 MATHICSE - Mathematics Institute of Computational Science and Engineering [Lausanne]
3 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche
4 IMT - Institut de Mathématiques de Toulouse UMR5219
5 INSA Lyon - Institut National des Sciences Appliquées de Lyon

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 $H^1(\Omega)$-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.

Keywords: Contact; Nitsche's method; Friction; Finite elements

Domains: Numerical Analysis [math.NA]

Franz Chouly, Mathieu Fabre, Patrick Hild, Rabii Mlika, Jerome Pousin, et al.. An overview of recent results on Nitsche's method for contact problems. UCL Workshop 2016, UCL (University College London), Jan 2016, London, United Kingdom. pp.93-141, ⟨10.1007/978-3-319-71431-8_4⟩. ⟨hal-01403003v1⟩