In two and three dimensional Lipschitz, but not necessarily convex, polytopal domains, we propose and analyze an a posteriori error estimator for an optimal control problem that involves the stationary Navier-Stokes equations; control constraints are also considered. The proposed error estimator is defined as the sum of three contributions, which are related to the discretization of the state and adjoint equations and the control variable. We prove that the devised error estimator is globally reliable and locally efficient. We conclude by presenting numerical experiments which reveal the competitive performance of an adaptive loop based on the proposed error estimator.

中文翻译：

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平稳 Navier-Stokes 方程分布式最优控制问题的后验误差估计

在二维和三维 Lipschitz（但不一定是凸的多面域）中，我们提出并分析了涉及平稳 Navier-Stokes 方程的最优控制问题的后验误差估计量；还考虑了控制约束。建议的误差估计量被定义为三个贡献的总和，这些贡献与状态和伴随方程以及控制变量的离散化有关。我们证明设计的误差估计器是全局可靠且局部有效的。我们通过展示数值实验得出结论，这些实验揭示了基于所提出的误差估计器的自适应回路的竞争性能。