SPACE-TIME SPECTRAL METHOD FOR AN OPTIMAL CONTROL PROBLEM GOVERNED BY A TWO-DIMENSIONAL PDE CONSTRAINT

In this paper, we solve a two-dimensional optimal control problem with a parabolic partial differential equation (PDE) constraint. First, the space-time spectral method is used to discretize time derivative and space derivative. Then the aforementioned problem is transformed into a solvable algebraic system. Since the spectral methods converge spectrally in both space and time, they have gained a significant attention in the last few decades. We prove that our method has exponential rates of convergence in both space and time.