Abstract
| Original language | English |
|---|---|
| Journal | IMA Journal of Numerical Analysis |
| DOIs | |
| Publication status | Published - 8 Jul 2019 |
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Keywords
- fluid mechanics
- finite element solution
- edge patches
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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 journal › Article
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
JF - IMA Journal of Numerical Analysis
SN - 0272-4979
ER -