期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 49, 期 4, 页码 1461-1481出版社
SIAM PUBLICATIONS
DOI: 10.1137/100794250
关键词
Navier-Stokes equations; finite element method; Scott-Vogelius elements; grad-div stabilization; strong mass conservation
资金
- National Science Foundation [DMS0914478]
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.
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