Robust stabilized Stokes approximation methods for highly stretched grids

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.