Mixed Methods for Optimal Control Problems

In this paper, we investigate a posteriori error estimates of amixed finite elementmethod for elliptic optimal control problems with an integral constraint. The gradient for ourmethod belongs to the square integrable space instead of the classical H(div; Ω) space. The state and co-state are approximated by the P ₀ ² -P₁ (velocity–pressure) pair and the control variable is approximated by piecewise constant functions. Using duality argument method and energy method, we derive the residual a posteriori error estimates for all variables.