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

Chouly, Franz; Hild, Patrick; Renard, Yves

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 503-528.

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 ($\theta$-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.

Classification : 65N12, 65N30, 74M15
Mots clés : Unilateral contact, elastodynamics, Nitsche’s method, time-marching schemes, stability

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