On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

D. Z. Turner, K. B. Nakshatrala, K. D. Hjelmstad

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal-order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid-based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions.

Original languageEnglish (US)
Pages (from-to)1291-1314
Number of pages24
JournalInternational Journal for Numerical Methods in Fluids
Volume60
Issue number12
DOIs
StatePublished - Aug 30 2009
Externally publishedYes

Keywords

  • Bubble functions
  • Finite elements for fluids
  • Mixed methods
  • Multi-scale formulation
  • Stabilized finite elements
  • Stokes equations

ASJC Scopus subject areas

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

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