A Nitsche-based method for unilateral contact problems: numerical analysis

摘要: We introduce a Nitsche-based formulation for the finite element discretization of unilateral contact problem in linear elasticity. It features weak treatment non-linear conditions through consistent penalty term. Without any additional assumption on set, we can prove theoretically its fully optimal convergence rate H1(Ω)-norm elements two dimensions, which is O(h^(1/2+ν)) when solution lies H^(3/2+ν)(Ω), 0 < ν ≤ 1/2. An interest that, conversely to Lagrange multiplier-based methods, no other unknown introduced and discrete inf-sup condition needs be satisfied.