A three-field formulation for incompressible viscoelastic fluids

Jaehyuk Kwack, Arif Masud

Research output: Contribution to journalArticlepeer-review


This paper presents a new stabilized finite element method for incompressible viscoelastic fluids. A three-field formulation is developed wherein Oldroyd-B model is coupled with the mass and momentum conservation equations for an incompressible viscous fluid. The variational multiscale (VMS) framework is employed to develop a stabilized formulation for the coupled momentum, continuity and stress equations. Based on the new stabilized method a family of linear and higher-order triangle and quadrilateral elements with equal-order velocity-pressure-stress fields is developed. Stability and convergence property of the various elements is studied and optimal rates are attained in the norms considered. The method is applied to some benchmark problems and accuracy and computational economy of the formulation is investigated for various flow conditions.

Original languageEnglish (US)
Pages (from-to)1413-1432
Number of pages20
JournalInternational Journal of Engineering Science
Issue number11
StatePublished - Nov 2010


  • Equal-order elements
  • Mixed finite elements
  • Oldroyd-B model
  • Stabilized methods
  • Three-field formulation
  • Variational multiscale methods
  • Viscoelastic fluids

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering


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