Unstable modes of the Q1-P0 element

Griffiths, David and Silvester, David (2011) Unstable modes of the Q1-P0 element. [MIMS Preprint]

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Abstract

In this paper the unstable eigenmodes of Q1-P0 velocity/pressure finite element approximation for incompressible flow problems are characterised. It is shown that the inf-sup stability constant is $O(h)$ in two dimensions and $O(h^2)$ in three dimensions. The basic tool in the analysis is the method of modified equations which is applied to finite difference representations of the underlying finite element equations. The asymptotic estimates are confirmed and supplemented by numerical experiments.

Item Type: MIMS Preprint
Additional Information: This item originally appeared as MCCM Report 257 in 1994.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: professor david silvester
Date Deposited: 16 Jun 2011
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1628

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