We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional Navier-Stokes-Voigt equations with a quadratic objective functional and box control constraints. The space-time error estimates of order $O(\sqrt{\tau}+h)$, where $\tau$ and $h$ are respectively the time and space discretization parameters, are proved for the difference between the locally optimal controls and their discrete approximations.

中文翻译：

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三维 Navier-Stokes-Voigt 方程最优控制问题的不连续伽辽金近似

我们分析了基于不连续（时间上）Galerkin 方法的完全离散方案，该方案与空间中的符合有限元子空间相结合，用于具有二次目标函数的三维 Navier-Stokes-Voigt 方程的分布式最优控制问题和框控制约束。证明$O(\sqrt{\tau}+h)$阶的时空误差估计，其中$\tau$和$h$分别是时间和空间离散化参数，证明了局部最优控制之间的差异以及它们的离散近似。