Summary.
An optimal control problem for impressed cathodic systems in electrochemistry 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 governing 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 of equations. Finally, we define a finite element algorithm and derive optimal error estimates.
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Received March 10, 1993 / Revised version received July 4, 1994
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Hou, L., Turner, J. Analysis and finite element approximation of an optimal control problem in electrochemistry with current density controls . Numer Math 71, 289–315 (1995). https://doi.org/10.1007/s002110050146
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DOI: https://doi.org/10.1007/s002110050146