A uniformly stable Fortin operator for the Taylor-Hood element
type: Item
instance of: scholarly article
title: A uniformly stable Fortin operator for the Taylor-Hood element
zbMATH Open document ID: 1261.65120
author: Joachim Schöberl
author: Ragnar Winther
author: Kent-Andre Mardal
published in: Numerische Mathematik
publication date: 2013-03-05T00:00:00Z
review text: The authors construct a new Fortin operator for the lowest order Taylor-Hood element in two space dimensions, which is uniformly stable both in \(L^2\) and \(H^1\). The construction is based on a tight connection between a subspace of the Taylor-Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the \(H^1\)-stability, while some mesh restrictions are imposed to obtain the \(L^2\)-stability. As a consequence of this construction, a uniform \(\inf\)-\(\sup\) condition associated the corresponding discretizations of a parameter dependent Stokes problem is obtained, and uniform bounds for a family of preconditioners for such problems, without relying on any extra regularity ensured by convexity of the domain can be verified.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65F08
zbMATH DE Number: 6141193
zbMATH Keywords: Fortin operator
zbMATH Keywords: Taylor-Hood element
zbMATH Keywords: regular triangulations
zbMATH Keywords: stability
zbMATH Keywords: \(\inf\)-\(\sup\) condition
zbMATH Keywords: Stokes problem
zbMATH Keywords: preconditioners
MaRDI profile type: Publication
full work available at URL: s00211-012-0492-6
OpenAlex ID: W2139094627
cites work: A stable finite element for the Stokes equations
cites work: Iterative techniques for time dependent Stokes problems
cites work: On the stability of the \(L^2\) projection in \(H^1(\omega)\)
cites work: Q4105995
cites work: Mixed and Hybrid Finite Element Methods
cites work: Some fast 3D finite element solvers for the generalized Stokes problem
cites work: Q4144698
cites work: On Bogovskiĭ and regularized Poincaré integral operators for de Rham complexes on Lipschitz domains
cites work: A Fortin operator for two-dimensional Taylor-Hood elements
cites work: Q4292463
cites work: Q3417969
cites work: Finite Element Methods for Navier-Stokes Equations
cites work: Regular decompositions for \(H(\mathrm{div})\) spaces
cites work: Preconditioning discretizations of systems of partial differential equations.
cites work: Uniform preconditioners for the time dependent Stokes problem
cites work: Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations
cites work: Efficient solvers for incompressible flow problems. An algorithmic and computational approach
DOI: 10.1007/S00211-012-0492-6
description: scientific article; zbMATH DE number 6141193