Galerkin spectral method for a fourth-order optimal control problem with H1-norm state constraint

Space-time spectral methods for a fourth-order parabolic optimal control problem in three control constraint cases

“…Up to now, a priori error analysis for spectral discretization of optimal control problems is debated in many publications, e.g., see Chen et al [5,8,14,22] for the second-order elliptic optimization problems, Zhou et al [33,34] and Tao et al [30] for the fourth-order elliptic optimization problems, [6] for optimal control problem governed by the Stokes equations. However, for the parabolic optimization problems, a priori error analysis for their space-time spectral discretization is very rare.…”