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2006.337: Fourier analysis of stabilised Q1-Q1 mixed finite element approximation

2006.337: Sean Norburn and David J. Silvester (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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DOI: 10.1137/S0036142999362274

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 2000 > 65 Numerical analysis
MIMS number:2006.337
Deposited By:Miss Louise Stait
Deposited On:17 August 2006

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