Local projection stabilized finite element method for Navier-Stokes equations
- 89 Downloads
This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.
Key wordslocal projection Navier-Stokes equations Reynolds number
Chinese Library ClassificationO242.21
2000 Mathematics Subject Classification65N30 76D05
Unable to display preview. Download preview PDF.
- Luo, K., Feng, M. F., and Wang, C. An accurate locking-free quadrilateral plate element (in Chinese). Journal of Sichuan University (Engeering Science Edition) 38(1), 44–48 (2006)Google Scholar
- Becker, R. and Braack, M. A two-level stabilization scheme for the Navier-Stokes equations. Numerical Mathematics and Advanced Applications (eds. Feistauer, M., Dolejší, V., Knobloch, P., and Najzar, K.), Springer-Verlag, Berlin Heidelberg, 123–130 (2003)Google Scholar