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

In a previous paper, we adapted Nitsche's method for 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 conditons. In the present paper we look at the stability properties of the above-mentioned schemes and we achieve 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.

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