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In this article, we develop a posteriori error analysis of a nonconformingfinite element method for a linear quadratic elliptic distributed optimalcontrol problem with two different set of constraints, namely (i) integralstate constraint and integral control constraint (ii) integral state constraintand pointwise control constraints. In the analysis, we have taken the approachof reducing the state-control constrained minimization problem into a stateminimization problem obtained by eliminating the control variable. Thereliability and efficiency of a posteriori error estimator are discussed.Numerical results are reported to illustrate the behavior of the errorestimator.

Adaptive finite element method for an elliptic optimal control problem with integral state constraints