Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations

✍ Scribed by Maxim Olshanskii; Gert Lube; Timo Heister; Johannes Löwe

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 635 KB
• Volume: 198
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2009.09.005

✦ Synopsis

In this paper the grad-div stabilization for the incompressible Navier-Stokes finite element approximations is considered from two different viewpoints: (i) as a variational multiscale approach for the pressure subgrid modeling and (ii) as a stabilization procedure of least-square type. Some new error estimates for the linearized problem with the grad-div stabilization are proved with the help of norms induced by the pressure Schur complement operator. We discuss the stabilization parameter choice arising in the frameworks of least-square and multiscale methods and consider assumptions which allow to relate both approaches.