In this article, we discuss a priori error estimates of a bubble enriched nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with integral state constraints. Therein, using the state equation we reduce the state-control constrained minimization problem to a pure state constrained minimization problem. We have obtained the optimal order (with respect to regularity) error estimates of finite element approximation in two cases: the optimal control problem with integral state constraints together with (i) integral control constraints (ii) pointwise control constraints. Numerical results are presented to confirm the theoretical findings.

在本文中，我们讨论了具有积分状态约束的线性二次椭圆分布最优控制问题的气泡丰富非一致性有限元方法的先验误差估计。其中，使用状态方程，我们将状态控制约束最小化问题简化为纯状态约束最小化问题。我们已经在两种情况下获得了有限元近似的最优阶（关于规律性）误差估计：具有积分状态约束的最优控制问题以及（i）积分控制约束（ii）逐点控制约束。给出了数值结果以证实理论发现。