A Numerical Method for Optimal Control-State Problem with Bivariate B-Spline Basis

We apply the bivariate B-spline basis to find an approximate solution for control-state function in a constrained optimal control problem, whose constraint is an elliptic partial differential equation (PDE) with Dirichlet boundary conditions. In this method, the PDE is first discretized and then by using bivariate B-spline basis, a state function is obtained with respect to some unknown coefficients. By applying generalized Newton method, the optimal value for the control function is also determined. Finally, a numerical example is given and the optimal solution is derived by using the bivariate B-spline basis.