Adaptive methods for frictionless contact problems

In this paper a posteriori error indicators for frictionless contact problems are presented. In detail, error indicators relying on superconvergence properties and error estimators based on duality principles are investigated. Applications are to 3D solids under the hypothesis of non-linear elastic material behaviour associated with finite deformations. A penalization technique is applied to enforce multilateral boundary conditions due to contact. The approximate solution of the problem is obtained by using the finite element method. Several numerical results are reported to show the applicability of the adaptive algorithm to the considered problems.