Local projection stabilized Galerkin approximations for the generalized Stokes problem

Kamel Nafa*, Andrew J. Wathen

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This, makes it a lot simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations.

Original languageEnglish
Pages (from-to)877-883
Number of pages7
JournalComputer Methods in Applied Mechanics and Engineering
Volume198
Issue number5-8
DOIs
Publication statusPublished - Jan 15 2009

Keywords

  • Convergence
  • Error estimates
  • Generalized Stokes equations
  • Local projection
  • Stabilized finite elements

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanical Engineering
  • Mechanics of Materials
  • Physics and Astronomy(all)

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