A posteriori error analysis of a domain decomposition algorithm for unilateral contact problem

In this paper, we consider a domain decomposition algorithm associated to a finite element method to approximate a unilateral frictionless contact problem between two elastic bodies. We present a global error estimator that takes into account of the error introduced by finite element analysis as well as the error introduced by the iterative resolution of the domain decomposition algorithm. The control of these error sources is a key point in order to introduce adaptive techniques and we propose error indicators that estimate the contribution of each source of error.