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

Abstract : 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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ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, 49 (2), pp.503-528
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Franz Chouly, Patrick Hild, Yves Renard. A Nitsche finite element method for dynamic contact : 2. Stability of the schemes and numerical experiments. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, 49 (2), pp.503-528. 〈hal-00958710〉

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