On gradient-type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi-harmonic equation

In this paper, a numerical method based on mixed finite element method for optimal boundary control problem governed by bi-harmonic equation is presented. The system of optimality equations consisting of state and costate function is derived. Based on the system, a gradient-type optimization method using a mixed finite approximation for solving the optimal boundary control is developed. In our algorithm, the trace of vortex function of costate equation on boundary plays a key role. Finally, a local error analysis at every iteration for this gradient-type optimization method is given.