Error estimates of the space-time spectral method for parabolic control problems

This work is devoted to investigate the spectral approximation of optimal control of parabolic problems. The space-time method is used to boost high-order accuracy by applying dual Petrov-Galerkin spectral scheme in time and spectral method in space. The optimality conditions are derived, and the a priori error estimates indicate the convergence of the proposed method. Numerical tests confirm the theoretical results, and show the efficiency of the method.