Local projection FEM stabilization for the time-dependent incompressible Navier-Stokes problem

Daniel Arndt, Helene Dallmann, Gert Lube

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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.

Original languageEnglish
Pages (from-to)1224-1250
Number of pages27
JournalNumerical Methods for Partial Differential Equations
Volume31
Issue number4
DOIs
StatePublished - Jul 1 2015
Externally publishedYes

Keywords

  • Navier-Stokes equations
  • Oseen equations
  • Smagorinsky model
  • incompressible flow
  • local projection stabilization
  • stabilized finite elements

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