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 0(h) in two dimensions and 0(h2)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.
|Name||Numerical Analysis Report|
|Publisher||Manchester Centre for Computational Mathematics|