Stabilised vs. stable mixed methods for incompressible flow

The accuracy of low-order mixed finite element methods for the incompressible Navier-Stokes equations is investigated in this work. Some numerical experiments suggest that the lowest-order stabilised P 1− P 0 method (linear velocity, constant pressure) is more efficient than the alternative a priori stable non-conforming Crouzeix-Raviart ( P −1− P 0) approach. The relative accuracy of stabilised P 1− P 0 and P 1− P 1, (linear velocity, continuous linear pressure) is assessed herein.