Franz Chouly, Patrick Hild, Vanessa Lleras, Yves Renard:
Nitsche method for contact with Coulomb friction: existence results for the static and dynamic finite element formulations
We study the Nitsche-based finite element method for contact with Coulomb friction considering both static and dynamic situations. We provide existence and/or uniqueness results for the discretized problems under appropriate assumptions on physical and numerical parameters. In the dynamic case, existence and uniqueness of the space semi-discrete problem holds for every value of the friction coefficient and the Nitsche parameter. In the static case, if the Nitsche parameter is large enough, existence is ensured for any friction coefficient, and uniqueness can be obtained provided that the friction coefficient is below a bound that depends on the mesh size. These results are complemented by a numerical study.
This preprint gave rise to the following definitive publication(s):
Franz CHOULY, Patrick HILD, Vanessa LLERAS, Yves RENARD: Nitsche method for contact with Coulomb friction: existence results for the static and dynamic finite element formulations. Journal of Computational and Applied Mathematics, vol. 416, paper no. 114557, (2022).