Optimal control of an evolutionary variational–hemivariational inequality model with new results in numerical analysis and control of the dynamic frictional contact problem

Abstract

In this paper, we are concerned with numerical analysis on optimal control of a dynamic contact model. Our work builds on some existing results of this model. We derive a weak formulation, and present an approximate problem for the weak formulation by discretization in space. We prove that the approximate problem has a unique solution, which converges to the unique solution of the original problem. The existence of optimal solutions to the control problem is established based on a known continuous dependence result. We consider the numerical solutions of the optimal control problem and prove a convergence result of numerical solutions.