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摘要
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 %26lt; nu %26lt;= 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.
- 出版日期2013
