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Pressure-robustness by commuting interpolation operators for Stokes discretizations with continuous pressures — arXiv:2609.18657

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.18657
License (as archived): CC0-1.0
Archived: 2026-10-15T15:48:54.585Z
SHA-256 of the archived text: 0482eb804587a79ab3c513046e9690f9e72193a2e1d974157dad95a222fcb873
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How to cite

Pressure-robustness by commuting interpolation operators for Stokes discretizations with continuous pressures — arXiv:2609.18657 — arXiv (en), https://arxiv.org/abs/2609.18657 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_43307dab1981 (Metraipolis archive dc_43307dab1981, sha256 0482eb804587a79ab3c513046e9690f9e72193a2e1d974157dad95a222fcb873)

BibTeX

@misc{dc43307dab1981,
  title = {Pressure-robustness by commuting interpolation operators for Stokes discretizations with continuous pressures — arXiv:2609.18657},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.18657},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_43307dab1981; sha256 0482eb804587a79ab3c513046e9690f9e72193a2e1d974157dad95a222fcb873},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.18657. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Common finite element discretizations for the incompressible Stokes equations with a continuous pressure approximation -- the MINI element, the Taylor--Hood element, or stabilized equal-order elements -- are not pressure-robust: the velocity error is polluted by the pressure best-approximation error, multiplied by the inverse viscosity. The established remedy replaces the test function in the momentum equation by a divergence-preserving reconstruction operator; for continuous pressure approximations this construction is cumbersome, requiring the solution of local problems (Lederer, Linke, Merdon & Schöberl, SIAM J. Numer. Anal., 2017). We propose a simpler alternative: interpolating the force by a Nédélec interpolation operator of suitable order instead of reconstructing the test function. Exploiting the commuting diagram property linking Nédélec and Lagrange interpolation operators, we show that the resulting method is pressure-robust for any $H^1$-conforming, continuous-pressure discretization. We give the complete analysis for the MINI element, and then for stabilized equal-order $P^kP^k$ elements of arbitrary degree $k$, proving that the interpolation-induced consistency error is pressure-robust and converges of optimal order. We validate the theory by several numerical examples.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-17 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.18657 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T15:09:07.971Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).