“…Therefore, there exist fruitful research results on this topic theoretically and numerically [4,34], especially for the elliptic optimal control problem [15,16,32]. Because of the large scale of discrete system and the limitation of computational resources, the design of the high accuracy mathematical scheme for parabolic optimal control problem is difficult, and we refer the readers to [1,18,19,20,21,22,23] and references therein. Based on the finite element approximation, the Crank-Nicolson scheme, the numerical integration formula, and the full Jacobian decomposition method with correction [1,17], an efficient numerical algorithm is proposed for the parabolic optimal control problem in this paper.…”