Preconditioning optimal control of the unsteady Burgers equations with H1H1 regularized term

In this paper, a new preconditioning technique along with MINRES in nonstandard inner product is designed for the linear system of equations arising from the unsteady Burgers equations constrained optimization problems. A new Schur complement approximation is provided. The eigenvalue bounds which verify the effectiveness of the Schur complement approximation are given. Numerical experiments show that the preconditioner using the new approximation Schur complement along with MINRES in nonstandard inner product works well in practice.