A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments

¹ Laboratoire de Mathématiques de Besançon – UMR CNRS 6623, Université de Franche Comté, 16 route de Gray, 25030 Besançon cedex, France
franz.chouly@univ-fcomte.fr
² Institut de Mathématiques de Toulouse - UMR CNRS 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, France
patrick.hild@math.univ-toulouse.fr
³ Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, 69621 Villeurbanne, France
yves.renard@insa-lyon.fr

Received: 13 March 2014
Revised: 1 September 2014

Abstract

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.