Variational and Numerical Analysis for an Electro-Viscoelastic Unilateral Contact Problem with Adhesion

In this paper we investigate a mathematical model for the unilateral contact between an electro-viscoelastic body and a conductive foundation. The Signorini conditions are used to model the contact, and adhesion between the contact surfaces is also taken into account. We establish the existence and uniqueness of a weak solution to this problem. Furthermore, we propose a fully discrete numerical scheme to approximate the solution, and we present and prove the main result concerning the estimation of errors.