An Overview of Recent Results on Nitsche's Method for Contact Problems

We summarize recent achievements in applying Nitsche's method to some contact and friction problems. We recall the setting of Nitsche's method in the case of unilateral contact with Tresca friction in linear elasticity. Main results of the numerical analysis are detailed: consistency, well-posedness, fully optimal convergence in H-1(Omega)/-norm, residual-based a posteriori error estimation. Some numerics and some recent extensions to multi-body contact, contact in large transformations and contact in elastodynamics are presented as well.