Abstract
We investigate the Galerkin spectral approximation of an optimal control problem governed by a fourth-order partial differential equation (PDE), in which an -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
-error estimate for the state and co-state but also
-error estimate for the control, state and co-state. Finally, three numerical examples are executed to validate the theoretical analysis.
Acknowledgements
The authors would like to thank the editor and the anonymous referees for their very careful reading and constructive suggestions that improve the manuscript substantially.
Disclosure statement
No potential conflict of interest was reported by the author(s).