L2-projected least-squares finite element methods for the Stokes equations

Huo-yuan Duan, Ping Lin, P. Saikrishnan, Roger C. E. Tan

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    Two new L2 least-squares (LS) finite element methods are developed for the velocity-pressure-vorticity first-order system of the Stokes problem with Dirichlet velocity boundary condition. A key feature of these new methods is that a local or almost local L2 projector is applied to the residual of the momentum equation. Such L2 projection is always defined onto the linear finite element space, no matter which finite element spaces are used for velocity-pressure-vorticity variables. Consequently, the implementation of this L2-projected LS method is almost as easy as that of the standard L2 LS method. More importantly, the former has optimal error estimates in L2-norm, with respect to both the order of approximation and the required regularity of the exact solution for velocity using equal-order interpolations and for all three variables (velocity, pressure, and vorticity) using unequal-order interpolations. Numerical experiments are given to demonstrate the theoretical results
    Original languageEnglish
    Pages (from-to)732-752
    Number of pages21
    JournalSIAM Journal on Numerical Analysis
    Volume44
    Issue number2
    DOIs
    Publication statusPublished - 2006

    Keywords

    • Stokes equation
    • Velocity-pressure-vorticity least-squares finite element method
    • L2 projection
    • Mass-lumping

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