Abstract Three different types of a posteriori error estimators are considered for the locally stabilised Stokes element P1-P0. The first is given by a norm of the residual, the second is obtained from the solution of local Stokes problems, and the third is obtained from the solution of local Poisson problems. All three estimators are shown to be equivalent to the true error independently of the choice of the stabilisation parameter, beta. An adaptive mesh refinement technique is given that creates meshes that conform to the requirements of the local stabilisation.
Some numerical results show that the estimators provide reasonable approximations to the true error.
They also show that the estimators are effective at detecting local singularities in the true solution. We assess the reliability of a simple a posteriori error estimator for steady state convection-diffusion equations in cases where convection dominates. Our estimator is computed by solving a local Poisson problem with Neumann boundary conditions. The 13th level of refinement for a convection-diffusion problem with an interior layer.