In this paper, we study variational discretization method for parabolic optimization problems. Firstly, we obtain some convergence and superconvergence analysis results of the approximation scheme. Secondly, we derive a posteriori error estimates of the approximation solutions. Finally, we present variational discretization approximation algorithm and adaptive variational discretization approximation algorithm for parabolic optimization problems and do some numerical experiments to confirm our theoretical results.

中文翻译：

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抛物线型最优控制问题的自适应变分离散逼近方法

本文研究抛物线优化问题的变分离散化方法。首先，我们获得了近似方案的一些收敛性和超收敛性分析结果。其次，我们得出了近似解的后验误差估计。最后，针对抛物线优化问题，提出了变分离散化近似算法和自适应变分离散化近似算法，并进行了一些数值实验，以验证我们的理论结果。