New approaches to error estimation and adaptivity for the Stokes and Oseenequations

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.