Fourier analysis of stabilised Q1-Q1 mixed finite element approximation

Norburn, Sean and Silvester, David J. (2001) Fourier analysis of stabilised Q1-Q1 mixed finite element approximation. SIAM Journal on Numerical Analysis, 39 (3). pp. 817-833. ISSN 0036-1429

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Abstract

We use Fourier analysis to investigate the instability of an equal-order mixed finite element approximation method for elliptic incompressible flow equations. The lack of stability can be attributed to the fact that the associated discrete Ladyzhenskaya--Babuska--Brezzi (LBB) constant tends to zero as the mesh size is reduced. We develop a stabilization approach that is appropriate to the periodic setting and deduce optimal choices of the associated stabilization parameter.

Item Type:	Article
Uncontrolled Keywords:	finite element; mixed approximation; stabilization
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	17 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/547

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