A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind

We consider an optimal control problem governed by elliptic variational inequality of the second kind. The is discretized linear finite elements for state and a discrete approach control. Based on quadratic growth condition we derive nearly priori error estimates. Moreover, establish order sufficient optimality conditions that ensure condition. These are rather restrictive, but allow us to construct one-dimensional locally solution with reduced regularity, which serves as exact numerical experiments.