Robust Stabilized Stokes Approximation Methods for Highly Stretched Grids

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

PDF IMAJNAlink.pdf Download (15kB)

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
Additional Information:	The DOI links directly to the published version of the paper.
Uncontrolled Keywords:	Stokes equations; mixed approximation; inf-sup stability; anisotropic grid refinement.
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	professor david silvester
Date Deposited:	09 Jun 2013
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1991

Actions (login required)

View Item