The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element
type: Item
instance of: scholarly article
title: The pressure-wired Stokes element: a mesh-robust version of the Scott-Vogelius element
author: Benedikt Gräßle
author: Nis-Erik Bohne
author: S. Sauter
published in: Numerische Mathematik
publication date: 2024-11-01T00:00:00Z
review text: The authors consider the numerical solution of the stationary Stokes equation in a bounded two-dimensional polygonal Lipschitz domain by a conforming Galerkin finite element method. The paper is outlined as follows. The Section 1 is an Introduction. After introducing the Stokes problem on the continuous as well as on the discrete level and the relevant notation in Section 2, the conforming pressure-wired Stokes element is defined in Section 3. The first main result in Section 4 establishes the discrete inf-sup condition for this new element with a lower bound on the inf-sup constant that is independent of \(h\), \(k\), and (nearly) critical points. The second main result controls the \(L^2\) norm of the divergence of the discrete velocity in Section. 5 and verifies its negligibility for small \(\eta \ll 1\). In Section 6 are reported numerical experiments of the convergence rates for the pressure-wired Stokes elements.
reviewed by: Temur Jangveladze
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 76M10
zbMATH DE Number: 7937501
zbMATH Keywords: Stokes equation
zbMATH Keywords: Scott-Vogelius element
MaRDI profile type: Publication
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DOI: 10.1007/S00211-024-01430-X
description: scientific article; zbMATH DE number 7937501