A posteriori error estimation for stabilised mixed approximations of the Stokes equations

The practical implementation of the lowest-order Pl - P0 (linear velocity, constant pressure) finite element method for the steady-state incompressible (Navier--)Stokes equations is addressed in this work. Three different types of a posteriori error indicator are introduced and each is shown to be equivalent to the discretization error. Our numerical results show that these indicators can be used to drive an adaptive refinement process which is specially tailored to create grids which conform to the requirements of the local stabilization. It is also shown that the indicators provide an effective method for detecting local singularities in the flow solution.