Incompressible flow modelling can be a dodgy business

This talk reviews some theoretical and practical aspects

of incompressible flow modelling using finite element approximations

of the (Navier-) Stokes equations.

The infamous Q1-P0 velocity/pressure mixed finite element approximation

method is discussed. Two practical ramifications of the inherent

instability are focused on, namely; the convergence of the approximation

with and without regularisation, and the behaviour of fast iterative

solvers (of multigrid type) applied to the pressure Poisson system

that arises when solving time-dependent Navier-Stokes equations

using classical projection methods.

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This is joint work with David Griffiths from the University of Dundee.