A posteriori error estimates of stabilized finite element method for the steady Navier–Stokes problem

In this paper we develop a posteriori error estimates for the steady Navier–Stokes equations based on the lowest equal-order mixed finite element pair. Residual type a posteriori error estimates are derived by means of general framework established by Verfürth for the nonlinear equations. Furthermore, a simple error estimator in L2L2 norm is also presented by using the duality argument. Numerical experiments using adaptive computations are presented to demonstrate the effectiveness of these error estimates for three examples. The first example is a singular problem with known solution, the second example is a physical model of lid driven cavity and the last one is a backward facing step problem.