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2011.80: Robust Stabilized Stokes Approximation Methods for Highly Stretched Grids

2011.80: David Silvester and Qifeng Liao (2013) Robust Stabilized Stokes Approximation Methods for Highly Stretched Grids. IMA Journal of Numerical Analysis, 33. pp. 413-431. ISSN 0272-4979

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DOI: 10.1093/imanum/drs012

Abstract

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-P0 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).

Item Type:Article
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Uncontrolled Keywords:Stokes equations; mixed approximation; inf-sup stability; anisotropic grid refinement.
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MSC 2000 > 76 Fluid mechanics
MIMS number:2011.80
Deposited By:professor david silvester
Deposited On:09 June 2013

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