Volume 49, Number 2, March-April 2015
|Page(s)||503 - 528|
|Published online||17 March 2015|
A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments
Laboratoire de Mathématiques de Besançon – UMR CNRS 6623,
Université de Franche Comté, 16
route de Gray, 25030
2 Institut de Mathématiques de Toulouse - UMR CNRS 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, France
3 Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, 69621 Villeurbanne, France
Received: 13 March 2014
Revised: 1 September 2014
In a previous paper [F. Chouly, P. Hild and Y. Renard, A Nitsche finite element method for dynamic contact. 1. Space semi-discretization and time-marching schemes. ESAIM: M2AN 49 (2015) 481–502.], we adapted Nitsche’s method to the approximation of the linear elastodynamic unilateral contact problem. The space semi-discrete problem was analyzed and some schemes (θ-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed under appropriate CFL conditions. In the present paper we look at the stability properties of the above-mentioned schemes and we proceed to the corresponding numerical experiments. In particular we prove and illustrate numerically some interesting stability and (almost) energy conservation properties of Nitsche’s semi-discretization combined to the new hybrid scheme.
Mathematics Subject Classification: 65N12 / 65N30 / 74M15
Key words: Unilateral contact / elastodynamics / Nitsche’s method / time-marching schemes / stability
© EDP Sciences, SMAI, 2015
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