A-POSTERIORI ERROR ESTIMATORS FOR THE STOKES AND OSEEN EQUATIONS

The problem of obtaining a posteriori estimates of the discretization Error when one uses finite element methods to approximate problems wit h an incompressibility constraint is discussed. A general approach to the treatment of the constraint condition and to the (possible) non-se lf-adjointness of the associated momentum equations is presented. A po steriori error estimates are derived for adaptive h, p, and h-p type f inite element schemes. Key features are that the local error residual problems are not subject to an incompressibility constraint thereby av oiding the need for special finite element schemes and that the analys is is valid far essentially any discretization scheme, including conti nuous and discontinuous pressure spaces. The estimator bounds the actu al error measured in an energy-like norm.