We derive space‐time a posteriori error estimates of finite element method for linear parabolic optimal control problems in a bounded convex polygonal domain. To discretize the control problem, we use piecewise linear and continuous finite elements for the approximations of the state and costate variables, whereas piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler implicit scheme. An elliptic reconstruction technique in conjunction with energy argument is used to derive a posteriori error estimates for the state, costate, and control variables in the L^∞(0,T;L²(Ω))‐norm. Moreover, numerical experiments are performed to illustrate the performance of the derived estimators.

中文翻译：

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抛物线型最优控制问题的时空有限元逼近后验误差分析：一种重构方法

对于有界凸多边形区域中的线性抛物最优控制问题，我们导出了时空有限元方法的后验误差估计。为了离散化控制问题，我们使用分段线性和连续有限元来近似状态变量和代价变量，而分段常数函数用于控制变量。时间离散化基于后向Euler隐式方案。与能量参数一起椭圆重建技术被用于导出的状态下，协状态，并控制在各变量的后验误差估计大号^∞（0，Ť ;大号²（Ω））-范数。此外，进行数值实验以说明导出的估计量的性能。