A posteriori error estimation for unilateral contact with matching and non-matching meshes

Abstract

In this paper, we consider the unilateral contact problem between elastic bodies. We propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the finite element approximation involving matching and non-matching meshes on the contact zone. The determination of the a posteriori error estimate is linked to the building of kinematically-admissible stress fields and statically-admissible stress fields. We then propose a finite element method for approximating the unilateral contact problem taking into account matching and non-matching meshes on the contact zone; then, we describe the construction of admissible fields. Lastly, we present optimized computations by using both the error estimates and a convenient mesh adaptivity procedure.