Name
Title | ||
|---|---|---|
A Connection Between Scott-Vogelius and Grad-Div Stabilized Taylor-Hood FE Approximations of the Navier-Stokes Equations |
Abstract | ||
|---|---|---|
This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. With a particular mesh construction, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein the first numerical tests of this element pair for the time dependent Navier-Stokes equations. We also prove that the limit of the grad-div stabilized Taylor-Hood solutions to the Navier-Stokes problem converges to the Scott-Vogelius solution as the stabilization parameter tends to infinity. That is, we provide theoretical justification that choosing the grad-div parameter large does not destroy the solution. Numerical tests are provided which verify the theory and show how both Scott-Vogelius and grad-div stabilized Taylor-Hood (with large stabilization parameter) elements can provide accurate results with excellent mass conservation for Navier-Stokes approximations. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/100794250 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
navier-stokes problem converges,numerical test,navier-stokes approximation,finite element computation,navier-stokes equations,time dependent navier-stokes equation,grad-div stabilized taylor-hood fe,navier-stokes equation,excellent mass conservation,element pair,scott-vogelius solution,scott-vogelius element pair,finite element method | Numerical tests,Mathematical optimization,Mathematical analysis,Approximations of π,Infinity,Finite element method,Mathematics,Conservation of mass,Navier–Stokes equations,Computation,Pointwise | Journal |
Volume | Issue | ISSN |
49 | 4 | 0036-1429 |
Citations | PageRank | References |
22 | 2.24 | 7 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael A. Case | 1 | 22 | 2.24 |
| Vincent J. Ervin | 2 | 118 | 15.66 |
| Alexander Linke | 3 | 92 | 12.29 |
| Leo G. Rebholz | 4 | 141 | 24.08 |