The talk discusses the benefits of pressure-robust discretizations in the scope of optimal control of incompressible flows. Here, gradient forces appearing 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. This is joint work with Christian Merdon (WIAS)
