论文标题
在最佳控制的背景下，压力自如
Pressure-robustness in the context of optimal control
论文作者
论文摘要
本文研究了压力自由离散的好处，这是对不可压缩流的最佳控制范围。数据中可能出现的梯度力可能会对状态和控制的准确性产生负面影响，并且只有在恢复了离散差异的无差异测试功能上，只有在其$ l^2 $ - 正交性上的$ l^2 $ - 正交性时才能正确平衡。这些测试功能的完全正交的无差异化离散或无差重构造可以做到这一点，并导致更好的先验估计值在数值示例中也得到了验证。
This paper studies the benefits of pressure-robust discretizations in the scope of optimal control of incompressible flows. Gradient forces that may appear in the data can have a negative impact on the accuracy of state and control and can only be correctly balanced if their $L^2$-orthogonality onto discretely divergence-free test functions is restored. Perfectly orthogonal divergence-free discretizations or divergence-free reconstructions of these test functions do the trick and lead to much better analytic a priori estimates that are also validated in numerical examples.
