  This paper develops efficient preconditioned iterative solvers for
incompressible flow problems discretised by an enriched Taylor-Hood mixed
approximation, in which the usual pressure space is augmented by a piecewise
constant pressure to ensure local mass conservation. This enrichment process
causes over-specification of the pressure when the pressure space is defined by
the union of standard Taylor-Hood basis functions and piecewise constant
pressure basis functions, which complicates the design and implementation of
efficient solvers for the resulting linear systems. We first describe the
impact of this choice of pressure space specification on the matrices involved.
Next, we show how to recover effective solvers for Stokes problems, with
preconditioners based on the singular pressure mass matrix, and for Oseen
systems arising from linearised Navier-Stokes equations, by using a two-stage
pressure convection-diffusion strategy. The codes used to generate the
numerical results are available online.
