WIAS Preprint No. 2923, (2022)

Pressure-robustness in the context of optimal control


Authors

  • Merdon, Christian
    ORCID: 0000-0002-3390-2145
  • Wollner, Winnifried

2020 Mathematics Subject Classification

  • 49M41 65N15 76D07

Keywords

  • optimization of incompressible fluids, Stokes equations, pressure-robustness, a priori error estimates

DOI

10.20347/WIAS.PREPRINT.2923

Abstract

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.

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