Pressure-Robustness in the Context of Optimal Control

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 -orthogonality onto discretely divergence-free test functions is restored. Perfectly orthogonal divergence-free discretizations or divergence-free reconstructions of these test functions lead to qualitatively better a priori estimates in the sense that the discrete velocities do not depend on the pressures scaled by the inverse of the viscosity. The consequences of the space discretization are also demonstrated and validated in numerical examples.