ANALYSIS AND FINITE-ELEMENT APPROXIMATION OF AN OPTIMAL-CONTROL PROBLEM IN ELECTROCHEMISTRY WITH CURRENT-DENSITY CONTROLS

An optimal control problem for impressed cathodic systems in electroch emistry is studied. The control in this problem is the current density on the anode. A matching objective functional is considered. We first demonstrate the existence and uniqueness of solutions for the governi ng partial differential equation with a nonlinear boundary condition. We then prove the existence of an optimal solution. Next, we derive a necessary condition of optimality and establish an optimality system o f equations. Finally, we define a finite element algorithm and derive optimal error estimates.