Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations

Howard Elman, Victoria E. Howle, John Shadid, David Silvester, Ray Tuminaro

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38 Scopus citations


This paper introduces two stabilization schemes for the least squares commutator (LSC) preconditioner developed by Elman, Howie, Shadid, Shuttleworth, and Tuminaro [SIAM J. Sci. Comput., 27 (2006), pp. 1651-1668] for the incompressible Navier-Stokes equations. This preconditioning methodology is one of several choices that are effective for Navier-Stokes equations, and it has the advantage of being defined from strictly algebraic considerations. It has previously been limited in its applicability to div-stable discretizations of the Navier-Stokes equations. This paper shows how to extend the same methodology to stabilized low-order mixed finite element approximation methods.

Original languageEnglish
Pages (from-to)290-311
Number of pages22
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2007


  • Iterative algorithms
  • Navier-Stokes
  • Preconditioning


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