Pressure-robustness in the context of optimal control
- Merdon, Christian
- Wollner, Winnifried
2020 Mathematics Subject Classification
- 49M41 65N15 76D07
- optimization of incompressible fluids, Stokes equations, pressure-robustness, a priori error estimates
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 L2-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.