Publication Date:
2013-04-11
Description:
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 Q 1 – P 0 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 Q 1 – 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).
Print ISSN:
0272-4979
Electronic ISSN:
1464-3642
Topics:
Mathematics
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