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

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

    Research output: Contribution to journalArticlepeer-review


    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. © 2007 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)290-311
    Number of pages21
    JournalSIAM Journal on Scientific Computing
    Issue number1
    Publication statusPublished - 2007


    • Iterative algorithms
    • Navier-Stokes
    • Preconditioning


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