Robust stabilized Stokes approximation methods for highly stretched grids

Qifeng Liao, David Silvester

    Research output: Contribution to journalArticlepeer-review


    Anisotropic meshes are important for efficiently resolving incompressible flow problems that include boundary layer or corner singularity phenomena. Unfortunately, the stability of standard inf-sup stable mixed approximation methods is prone to degeneracy whenever the mesh aspect ratio becomes large. As an alternative, a stabilized mixed approximation method is considered here. Specifically, a robust a priori error estimate for the local jump stabilized Q1-P0 approximation introduced by Kechkar & Silvester (1992, Analysis of locally stabilized mixed finite element methods for the Stokes problem. Math. Comp., 58, 1-10) is established for anisotropic meshes. Our numerical results demonstrate that the stabilized Q1-P 0 method is competitive with the nonconforming, nonparametric, rotated approximation method introduced by Rannacher & Turek (1992, Simple nonconforming quadrilateral Stokes element. Numer. Meth. Partial Differential Equations, 8, 97-111). © 2012 The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
    Original languageEnglish
    Pages (from-to)413-431
    Number of pages18
    JournalIMA Journal of Numerical Analysis
    Issue number2
    Publication statusPublished - Apr 2013


    • anisotropic grid refinement
    • inf-sup stability
    • mixed approximation
    • Stokes equations


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