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

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wias_preprints_3097.pdf (1.3 MB)

Date

2024

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Advisor

Volume

3097

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Journal

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WIAS Preprints

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Publisher

Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik

Supplementary Material

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https://doi.org/10.1016/j.aml.2024.109138

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https://doi.org/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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Keywords

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

Keywords GND

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Report

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publishedVersion

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https://oa.tib.eu/renate/handle/123456789/34582
 https://doi.org/10.34657/33650

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Mathematik
WIAS Preprints

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