A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem

Abstract We present a new residual-type a posteriori error estimator for the discontinuous finite element solution of contact problems. The theoretical results are derived for two and three-dimensional domains and arbitrary gap functions. The estimator yields upper and lower bounds to a suitable error notion which measures the error in the displacements and in a quantity related to the contact stresses and the actual contact zone. In the derivation of the error estimator the local properties of the discontinuous solution are exploited appropriately so that, on the one hand, the error estimator has no contributions related to the non-linearity in the interior of the actual contact zone and, on the other hand, the critical region between the actual and non-actual contact zone can be well refined.