Stability of some low-order approximations for the Stokes problem

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2 Citations (Scopus)

Abstract

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
Volume56
Issue number6
DOIs
Publication statusPublished - Feb 28 2008

Keywords

  • Error estimates
  • Finite elements
  • Stability
  • Stokes equations

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics
  • Condensed Matter Physics

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