积分状态约束椭圆型最优控制问题的自适应有限元法
Adaptive finite element method for an elliptic optimal control problem with integral state constraints
摘要：
本文对线性二次椭圆分布最优控制问题的离散有限元法进行了后验误差分析，该问题具有两组不同的约束条件：（i）积分状态约束和积分控制约束;（ii）积分状态约束和逐点控制约束。在分析中，我们采用了将状态控制约束最小化问题转化为通过消除控制变量而得到的状态最小化问题的方法。讨论了后验误差估计的可靠性和有效性。数值结果报告，以说明的误差估计的行为。
英文摘要：
In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint and integral control constraint (ii) integral state constraint and pointwise control constraints. In the analysis, we have taken the approach of reducing the state-control constrained minimization problem into a state minimization problem obtained by eliminating the control variable. The reliability and efficiency of a posteriori error estimator are discussed. Numerical results are reported to illustrate the behavior of the error estimator.
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