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Symmetric and non-symmetric variants of Nitsche's method for contact problems in elasticity: theory and numerical experiments


Authors: Franz Chouly, Patrick Hild and Yves Renard
Journal: Math. Comp. 84 (2015), 1089-1112
MSC (2010): Primary 65N12, 65N30, 74M15
DOI: https://doi.org/10.1090/S0025-5718-2014-02913-X
Published electronically: October 31, 2014
MathSciNet review: 3315501
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Abstract: A general Nitsche method, which encompasses symmetric and non-symmetric variants, is proposed for frictionless unilateral contact problems in elasticity. The optimal convergence of the method is established both for two- and three-dimensional problems and Lagrange affine and quadratic finite element methods. Two- and three-dimensional numerical experiments illustrate the theory.


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Additional Information

Franz Chouly
Affiliation: Laboratoire de Mathématiques de Besançon - UMR CNRS 6623, Université de Franche Comté, 16 route de Gray, 25030 Besançon Cedex, France
Email: franz.chouly@univ-fcomte.fr

Patrick Hild
Affiliation: Institut de Mathématiques de Toulouse - UMR CNRS 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Email: patrick.hild@math.univ-toulouse.fr

Yves Renard
Affiliation: Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France
Email: yves.renard@insa-lyon.fr

DOI: https://doi.org/10.1090/S0025-5718-2014-02913-X
Keywords: Unilateral contact, finite elements, Nitsche's method
Received by editor(s): January 14, 2013
Received by editor(s) in revised form: September 4, 2013
Published electronically: October 31, 2014
Article copyright: © Copyright 2014 American Mathematical Society