Error estimation for low-order adaptive finite element approximations for fluid flow problems

We derive computable a posteriori error estimates for a wide family of low-order conforming and conforming stabilized finite element approximations for fluid flow problems. The estimators provide upper bounds on the error measured in natural energy-type norms. The analysis combines a Ritz projection of the residuals of the equation with explicit solutions of a local Neumann-type problem which required the introduction of suitable equilibrated fluxes. We provide a general framework in two and three dimensions with explicit formulas, which can be used to implement adaptive procedures. Finally, several numerical experiments are presented to test the performance of the error estimators.