Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: theory and numerical experiments

A general Nitsche method, which encompasses symmetric and non-symmetric variants, is proposed for frictionless unilateral contact problems in elasticity. The optimal convergence of the method is established both for two- and three-dimensional problems and Lagrange affine and quadratic finite element methods. Two- and three-dimensional numerical experiments illustrate the theory.