Stability of a trilinear-trilinear approximation for the Stokes equations

Kamel Nafa, Nouressadat Touafek

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1 Citation (Scopus)

Abstract

The choice of mixed finite element approximations for fluid flow problems is a compromise between accuracy and computational efficiency. Although a number of finite elements are found in the literature only few low-order approximations are stable. This is particularly true for three-dimensional flow problems. These elements are attractive because of their simplicity and efficiency, but can suffer though poor rate of convergence. In this paper the stability of a continuous trilinear-trilinear approximation is being analysed for general geometries. Using the macroelement technique, we prove the stability of the approximation. As a result, optimal rates of convergence are obtained for both the velocity and pressure approximations.

Original languageEnglish
Pages (from-to)325-332
Number of pages8
JournalCommunications in Numerical Methods in Engineering
Volume19
Issue number5
DOIs
Publication statusPublished - May 2003

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Keywords

  • Error estimates
  • Finite elements
  • Stability
  • Stokes equations

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

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