We present a new approach to deliver reliable approximations of the norm of
the residuals resulting from finite element solutions to the Stokes and Os
een equations. The method is based upon a global solve in a bubble space us
ing iterative techniques. This provides an alternative to the classical equ
ilibrated element residual methods for which it is necessary to construct p
roper boundary conditions for each local problem. The method is first used
to develop a global a posteriori error estimator. It is then applied in a s
trategy to control the numerical error in specific outputs or quantities of
interest which are functions of the solutions to the Stokes and Oseen equa
tions. Copyright (C) 1999 John Wiley & Sons, Ltd.