The Penalty Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem
This work provides a new numerical method for contact mechanics problems, offering a penalty-free approach that may simplify implementation and improve accuracy.
The authors propose a penalty-free Nitsche method for the Signorini contact problem, using a nonlinear displacement-based contact condition and nonsymmetric Nitsche formulation, achieving optimal error estimates with nonconforming finite elements.
We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces. The contact condition is then imposed using the nonsymmetric variant of Nitsche's method that does not require a penalty term for stability. Nonconforming piecewise affine elements are considered for the bulk discretization. We prove optimal error estimates in the energy norm.