Stability of some low-order approximations for the Stokes problem

Kamel Nafa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Two-level low-order finite element approximations are considered for the inhomogeneous Stokes equations. The elements introduced are attractive because of their simplicity and computational efficiency. In this paper, the stability of a Q1(h)-Q1(2h) approximation is analysed for general geometries. Using the macroelement technique, we prove the stability condition for both two- and three-dimensional problems. As a result, optimal rates of convergence are found for the velocity and pressure approximations. Numerical results for three test problems are presented. We observe that for the computed examples, the accuracy of the two-level bilinear approximation is compared favourably with some standard finite elements.

Original languageEnglish
Pages (from-to)753-765
Number of pages13
JournalInternational Journal for Numerical Methods in Fluids
Issue number6
Publication statusPublished - Feb 28 2008


  • Error estimates
  • Finite elements
  • Stability
  • Stokes equations

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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