A POSTERIORI ERROR ESTIMATES FOR PRESSURE-CORRECTION SCHEMES

A posteriori error estimates for time discretization of the incompressible Stokes equations by pressure-correction methods are presented. We rigorously prove global upper bounds for the incremental backward Euler scheme as well as for the two-step backward differential formula method (BDF2) in rotational form. Moreover, rate optimality of the estimators is stated for velocity (in the case of backward Euler and BDF2 in rotational form) and pressure (in the case of Euler). Computational experiments confirm the theoretical results.