This work is motivated by recent interest in the topic of pointwise tracking type optimal control problems for the Stokes problem. Pointwise tracking consists of point evaluations in the objective functional which lead to Dirac measures appearing as source terms of the adjoint problem. Considering bounds for the control allows for improved regularity results for the exact solution and improved approximation error estimates of its numerical counterpart. We show a sub-optimal convergence result in three dimensions that nonetheless improves the results known from the literature. Finally, we offer supporting numerical experiments and insights towards optimal approximation error estimates.

中文翻译：

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改进的误差估计，可在三个维度上进行逐点跟踪，以最佳控制斯托克斯问题

这项工作是受最近对Stokes问题的逐点跟踪型最优控制问题的兴趣所激发。逐点跟踪由目标函数中的点评估组成，这导致狄拉克度量出现为伴随问题的源项。考虑到控制范围，可以改善精确解的规则性结果，并改善其数值对应项的近似误差估计。我们在三个维度上显示了次优的收敛结果，但仍改进了文献中已知的结果。最后，我们提供支持的数值实验和对最佳逼近误差估计的见解。