A LEGENDRE-GALERKIN SPECTRAL METHOD FOR OPTIMALCONTROL PROBLEMS GOVERNED BY ELLIPTIC EQUATIONS

摘要

In this paper, we study the Legendre–Galerkin spectral approximation for a con-strained optimal control problem. We first derive a priori error estimates for the spectral approx-imation of optimal control problems. Then a posteriori error estimates are obtained for both thestate and the control approximation. A preconditioning projection algorithm is proposed with somenumerical tests.