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 (-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.
DOI : 10.1051/m2an/2014046
Mots clés : Unilateral contact, elastodynamics, Nitsche’s method, time-marching schemes, stability
@article{M2AN_2015__49_2_503_0, author = {Chouly, Franz and Hild, Patrick and Renard, Yves}, 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}, publisher = {EDP-Sciences}, volume = {49}, number = {2}, year = {2015}, doi = {10.1051/m2an/2014046}, zbl = {1311.74114}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014046/} }
TY - JOUR AU - Chouly, Franz AU - Hild, Patrick AU - Renard, Yves TI - A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 503 EP - 528 VL - 49 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014046/ DO - 10.1051/m2an/2014046 LA - en ID - M2AN_2015__49_2_503_0 ER -
%0 Journal Article %A Chouly, Franz %A Hild, Patrick %A Renard, Yves %T A Nitsche finite element method for dynamic contact: 2. Stability of the schemes and numerical experiments %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 503-528 %V 49 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014046/ %R 10.1051/m2an/2014046 %G en %F M2AN_2015__49_2_503_0
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. http://www.numdam.org/articles/10.1051/m2an/2014046/
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