Abstract
We consider conforming finite element (FE) approximations of the time‐dependent, incompressible Navier–Stokes problem with inf‐sup stable approximation of velocity and pressure. In case of high Reynolds numbers, a local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence‐free constraint. For the arising nonlinear semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies and Tobiska (IMA J. Numer. Anal., to appear) for the linearized model and takes partly advantage of the analysis in Burman and Fernández, Numer. Math. 107 (2007), 39–77 for edge‐stabilized FE approximation of the Navier–Stokes problem. Some numerical experiments complement the theoretical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1224–1250, 2015
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Numerical Methods for Partial Differential Equations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
