Pressure-improved Scott-Vogelius type elements

Fuente: arXiv
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Auteurs principaux: Bohne, Nis-Erik, Gräßle, Benedikt, Sauter, Stefan A.
Format: Preprint
Publié: 2024
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author Bohne, Nis-Erik
Gräßle, Benedikt
Sauter, Stefan A.
author_facet Bohne, Nis-Erik
Gräßle, Benedikt
Sauter, Stefan A.
contents The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.
format Preprint
id arxiv_https___arxiv_org_abs_2403_04499
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Pressure-improved Scott-Vogelius type elements
Bohne, Nis-Erik
Gräßle, Benedikt
Sauter, Stefan A.
Numerical Analysis
65N30, 65N12, 76D07
The Scott-Vogelius element is a popular finite element for the discretization of the Stokes equations which enjoys inf-sup stability and gives divergence-free velocity approximation. However, it is well known that the convergence rates for the discrete pressure deteriorate in the presence of certain $critical$ $vertices$ in a triangulation of the domain. Modifications of the Scott-Vogelius element such as the recently introduced pressure-wired Stokes element also suffer from this effect. In this paper we introduce a simple modification strategy for these pressure spaces that preserves the inf-sup stability while the pressure converges at an optimal rate.
title Pressure-improved Scott-Vogelius type elements
topic Numerical Analysis
65N30, 65N12, 76D07
url https://arxiv.org/abs/2403.04499