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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2015

A Nitsche finite element method for dynamic contact : 1. Semi-discrete problem analysis and time-marching schemes

Résumé

This paper presents a new approximation of elastodynamic frictionless contact problems based both on the finite element method and on an adaptation of Nitsche's method which was initially designed for Dirichlet's condition. A main interesting characteristic is that this approximation produces well-posed space semi-discretizations contrary to standard finite element discretizations. This paper is then mainly devoted to present an analysis of the semi-discrete problem in terms of consistency, well-posedness and energy conservation, and also to study the well-posedness of some time-marching schemes (theta-scheme, Newmark and a new hybrid scheme). The stability properties of the schemes and the corresponding numerical experiments can be found in a second paper.
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Dates et versions

hal-00958695 , version 1 (13-03-2014)

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Franz Chouly, Patrick Hild, Yves Renard. A Nitsche finite element method for dynamic contact : 1. Semi-discrete problem analysis and time-marching schemes. ESAIM: Mathematical Modelling and Numerical Analysis, 2015, 49 (2), pp.481-502. ⟨10.1051/m2an/2014041⟩. ⟨hal-00958695⟩
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