Galerkin spectral approximation for optimal control problem of a fourth-order equation with L2-norm control constraint.

We investigate the Galerkin spectral approximation of an optimal control problem governed by a fourth-order partial differential equation (PDE), in which an L 2 -norm constraint on control variable is equipped. First, the optimality conditions for both the original control problem and its spectral approximation problem are, respectively, obtained. Then, a priori error estimates of the spectral approximation problem are established in detail. Next, a posteriori error estimates for the approximation problem are also investigated, which include not only H 2 -error estimate for the state and co-state but also L 2 -error estimate for the control, state and co-state. Finally, three numerical examples are executed to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]