Geodesic
A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments
Chouly, Franz1  ; Hild, Patrick2  ; Renard, Yves3 
1 Laboratoire de Mathématiques de Besançon – UMR CNRS 6623, Université de Franche Comté, 16 route de Gray, 25030 Besançon cedex, France
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
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 503-528

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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.

Reçu le :
DOI : 10.1051/m2an/2014046
Classification : 65N12, 65N30, 74M15
Keywords: Unilateral contact, elastodynamics, Nitsche’s method, time-marching schemes, stability

Chouly, Franz 1 ; Hild, Patrick 2 ; Renard, Yves 3

1 Laboratoire de Mathématiques de Besançon – UMR CNRS 6623, Université de Franche Comté, 16 route de Gray, 25030 Besançon cedex, France
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 
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     title = {A {Nitsche} finite element method for dynamic contact: 2. {Stability} of the schemes and numerical experiments},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {503--528},
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Chouly, Franz; Hild, Patrick; Renard, Yves. A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 503-528. doi: 10.1051/m2an/2014046

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