A new two-grid P₀²-P₁ mixed finite element algorithm for general elliptic optimal control problems

In this paper, a new two-grid mixed finite element scheme for distributed optimal control governed by general elliptic equations is presented. P 2 0 -P 1 mixed finite elements and piecewise constant functions are used for spatial discretization. Convergence of the proposed two-grid algorithm is discussed. In the two-grid scheme, the solution of the elliptic optimal control problem on a fine grid is reduced to the solution of the elliptic optimal control problem on a much coarser grid and the solution of a symmetric linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy.