An adaptive finite element approach for frictionless contact problems

The derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and in nitesimal deformation is presented. The approximated solution of this problem is obtained by using the nite element method. A penalization or augmented-Lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary. An a posteriori error estimator suitable for adaptive mesh re nement in this problem is proposed, together with its mathematical justi cation. Up to the present time, this mathematical proof is restricted to the penalization approach. Several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators.