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We design and analyse a Nitsche method for contact problems. Compared to theseminal work of Chouly and Hild (A Nitsche-based method for unilateral contactproblems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our methodis constructed by expressing the contact conditions in a nonlinear function forthe displacement variable instead of the lateral forces. The contact conditionis then imposed using the nonsymmetric variant of Nitsche's method that doesnot require a penalty term for stability. Nonconforming piecewise affineelements are considered for the bulk discretization. We prove optimal errorestimates in the energy norm.

The Penalty Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem