A NITSCHE-BASED METHOD FOR UNILATERAL CONTACT PROBLEMS: NUMERICAL ANALYSIS

We introduce a Nitsche-based finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the nonlinear contact conditions through a consistent penalty term. Without any additional assumption on the contact set, we can prove theoretically its fully optimal convergence rate in the H-1(Omega)-norm for linear finite elements in two dimensions, which is O(h(1/2 + nu)) when the solution lies in H3/2 + nu(Omega), 0 < nu <= 1/2. An interest of the formulation is that, as opposed to Lagrange multiplier-based methods, no other unknown is introduced and no discrete inf-sup condition needs to be satisfied.