WIAS Preprint No. 3097, (2024)

Pressure-robust L2 ($Omega$) error analysis for Raviart--Thomas enriched Scott--Vogelius pairs


Authors

  • John, Volker
    ORCID: 0000-0002-2711-4409
  • Li, Xu
  • Merdon, Christian
    ORCID: 0000-0002-3390-2145

2020 Mathematics Subject Classification

  • 65N15 65N30 76M10

2010 Physics and Astronomy Classification Scheme

  • 47.10.ad 47.11.F

Keywords

  • Stokes equations, finite element method, stabilization, divergence-free, pressure-robust L2 velocity, error analysis

DOI

10.20347/WIAS.PREPRINT.3097

Abstract

Recent work shows that it is possible to enrich the Scott--Vogelius finite element pair by cer- tain Raviart--Thomas functions to obtain an inf-sup stable and divergence-free method on general shape-regular meshes. A skew-symmetric consistency term was suggested for avoiding an ad- ditional stabilization term for higher order elements, but no L2 (Ω) error estimate was shown for the Stokes equations. This note closes this gap. In addition, the optimal choice of the stabilization parameter is studied numerically.

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