WIAS Preprint No. 3055, (2023)

Augmenting the grad-div stabilization for Taylor--Hood finite elements with a vorticity stabilization


Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Merdon, Christian
    ORCID: 0000-0002-3390-2145
  • Zainelabdeen, Marwa

2020 Mathematics Subject Classification

  • 49M41 65N15 76D07

2010 Physics and Astronomy Classification Scheme

  • 47.10.ad 47.11.Fg

Keywords

  • Oseen equations, pressure-robustness, finite element methods, a priori error estimates, convection robustness

DOI

10.20347/WIAS.PREPRINT.3055

Abstract

The least squares vorticity stabilization (LSVS), proposed in Ahmed et al. for the Scott--Vogelius finite element discretization of the Oseen equations, is studied as an augmentation of the popular grad-div stabilized Taylor--Hood pair of spaces. An error analysis is presented which exploits the situation that the velocity spaces of Scott--Vogelius and Taylor--Hood are identical. Convection-robust error bounds are derived under the assumption that the Scott--Vogelius discretization is well posed on the considered grid. Numerical studies support the analytic results and they show that the LSVS-grad-div method might lead to notable error reductions compared with the standard grad-div method.

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