This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization method. The state equation is discretized by a space-time finite element method. The controls are not discretized. Under suitable assumptions optimal convergence rates for the error in the state and control variable are proven. Based on a conditional gradient method the solution of the semi-discretized optimal control problem is computed. The theoretical convergence rates are confirmed in a numerical example.

中文翻译：

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具有波动范围控制的波动方程控制的最优控制问题的最优有限元误差估计

这项工作讨论了有限时间离散的线性波动方程的最优控制问题的有限元离散化。主要关注离散化方法的收敛性分析。状态方程通过时空有限元方法离散化。控件不离散化。在适当的假设下，证明了状态和控制变量误差的最佳收敛速度。基于条件梯度法，计算了半离散最优控制问题的解。数值示例证实了理论收敛速度。