A posteriori error control of finite element approximations for Coulomb's frictional contact

This paper is concerned with the frictional unilateral contact problem gove rned by Coulombs law. We define an a posteriori error estimator based on th e concept of error in the constitutive relation to quantify the accuracy of a finite element approximation of the problem. We propose and study differ ent mixed finite element approaches and discuss their properties in order t o compute the estimator. The information given by the error estimates is th en coupled with a mesh adaptivity technique which provides the user with th e desired quality and minimizes the computation costs. The numerical implem entation of the error estimator as well as optimized computations are perfo rmed.