Improved local projection for the generalized stokes problem

Research output: Contribution to journalArticle

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 methods is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although the 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 much 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)862-873
Number of pages12
JournalAdvances in Applied Mathematics and Mechanics
Volume1
Issue number6
DOIs
Publication statusPublished - 2009

Fingerprint

Stokes Problem
Projection
Stabilized Methods
Stabilized Finite Element Method
Optimal Rate of Convergence
Stokes Equations
Interpolants
Stability and Convergence
Pressure Gradient
Pressure gradient
Convergence Properties
System of equations
Finite element method
Unknown
Approximation

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering

Cite this

Improved local projection for the generalized stokes problem. / Nafa, Kamel.

In: Advances in Applied Mathematics and Mechanics, Vol. 1, No. 6, 2009, p. 862-873.

Research output: Contribution to journalArticle

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