A locally conservative, discontinuous least-squares finite element method for the Stokes equations

Pavel Bochev, James Lai, Luke Olson

Research output: Contribution to journalArticlepeer-review

Abstract

Conventional least-squares finite element methods (LSFEMs) for incompressible flows conserve mass only approximately. For some problems, mass loss levels are large and result in unphysical solutions. In this paper we formulate a new, locally conservative LSFEM for the Stokes equations wherein a discrete velocity field is computed that is point-wise divergence free on each element. The central idea is to allow discontinuous velocity approximations and then to define the velocity field on each element using a local stream-function. The effect of the new LSFEM approach on improved local and global mass conservation is compared with a conventional LSFEM for the Stokes equations employing standard C 0 Lagrangian elements.

Original languageEnglish (US)
Pages (from-to)782-804
Number of pages23
JournalInternational Journal for Numerical Methods in Fluids
Volume68
Issue number6
DOIs
StatePublished - Feb 29 2012

Keywords

  • Discontinuous elements
  • Least-squares finite element methods
  • Locally conservative
  • Pressure
  • Stokes equations
  • Stream-function
  • Vorticity

ASJC Scopus subject areas

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

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