The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes

Gabriel R Barrenechea, Andreas Wachtel

Research output: Contribution to journalArticle

Abstract

Uniform LBB conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier-Stokes equations. In this work we prove a uniform inf-sup condition for the lowest order Taylor-Hood pairs Q2×Q1 and P2×P1 on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalise Verf ̈urth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.
LanguageEnglish
JournalIMA Journal of Numerical Analysis
DOIs
Publication statusPublished - 8 Jul 2019

Fingerprint

Anisotropic Mesh
Fluid mechanics
Navier Stokes equations
Patch
Lowest
Inf-sup Condition
Uniform Stability
Fluid Mechanics
Finite Element Solution
Stokes
Stability Condition
Incompressible Fluid
Navier-Stokes Equations
Mesh
Generalise
Necessary
Sufficient Conditions

Keywords

  • fluid mechanics
  • finite element solution
  • edge patches

Cite this

@article{837a37ee7eac4b1783533c0883c52fb8,
title = "The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes",
abstract = "Uniform LBB conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier-Stokes equations. In this work we prove a uniform inf-sup condition for the lowest order Taylor-Hood pairs Q2×Q1 and P2×P1 on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalise Verf ̈urth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.",
keywords = "fluid mechanics, finite element solution, edge patches",
author = "Barrenechea, {Gabriel R} and Andreas Wachtel",
year = "2019",
month = "7",
day = "8",
doi = "10.1093/imanum/drz028",
language = "English",
journal = "IMA Journal of Numerical Analysis",
issn = "0272-4979",

}

The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes. / Barrenechea, Gabriel R; Wachtel, Andreas.

In: IMA Journal of Numerical Analysis , 08.07.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes

AU - Barrenechea, Gabriel R

AU - Wachtel, Andreas

PY - 2019/7/8

Y1 - 2019/7/8

N2 - Uniform LBB conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier-Stokes equations. In this work we prove a uniform inf-sup condition for the lowest order Taylor-Hood pairs Q2×Q1 and P2×P1 on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalise Verf ̈urth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

AB - Uniform LBB conditions are of fundamental importance for the finite element solution of problems in incompressible fluid mechanics, such as the Stokes and Navier-Stokes equations. In this work we prove a uniform inf-sup condition for the lowest order Taylor-Hood pairs Q2×Q1 and P2×P1 on a family of affine anisotropic meshes. These meshes may contain refined edge and corner patches. We identify necessary hypotheses for edge patches to allow uniform stability and sufficient conditions for corner patches. For the proof, we generalise Verf ̈urth’s trick and recent results by some of the authors. Numerical evidence confirms the theoretical results.

KW - fluid mechanics

KW - finite element solution

KW - edge patches

U2 - 10.1093/imanum/drz028

DO - 10.1093/imanum/drz028

M3 - Article

JO - IMA Journal of Numerical Analysis

T2 - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

ER -