A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis

We introduce a Nitsche-based formulation for the finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the non-linear 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(Ω)norm for linear finite elements in two dimensions, which is O(h 1 2) when the solution lies in H 3 2(Ω), 0 < ν ≤ 1/2. An interest of the formulation is that, conversely to Lagrange multiplier-based methods, no other unknown is introduced and no discrete inf–sup condition needs to be satisfied.