INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, VOL. 27, 33±39 (1998) LOCAL AND POLLUTION ERROR ESTIMATION FOR STOKESIAN FLOWS J. TINSLEY ODEN 1 * , YUSHENG FENG 2 AND SERGE PRUDHOMME 1 1 Texas Institute for Computational and Applied Mathematics (TICAM), 3500 W Balcones Ctr Dr, MCC 3 11040, Austin, TX 78712, U.S.A. 2 Motorola, Inc., Predictive Engineering Lab., Austin, TX. 78721, U.S.A. SUMMARY We describe in this paper an algebraic technique for estimating local and pollution errors in ®nite element approximations of Stokesian ¯ows. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 27: 33±39 (1998) KEY WORDS: error estimation; Stokes ¯ow; adaptivity 1. INTRODUCTION The impact of adaptive methods on computational ¯uid dynamics is well recognized and can be regarded as one of the most important developments in CFD in several decades. The idea behind these approaches is to develop methods for error estimation (or error indication) and to use such estimates as a basis for adapting the mesh to reduce, control or equidistribute the numerical error. There is a large and still growing volume of evidence that such approaches can be highly effective and reduce substantially the number of unknowns needed in a given simulation to achieve a target error level; these approaches have even been successful in p- and hp-version ®nite element approximations. 1±5 In recent times the success of adaptive schemes and a posteriori error estimation methods has prompted users to demand more information from such devices. In addition to giving rough estimates suf®cient to deliver good meshes for controlling global approximations of energy or entropy, the need for determining local errors in energy norms or in other norms is persistently expressed. Moreover, there is naturally interest in determining errors in components of solutions of vector-valued functions, directional errors and elementwise errors in various norms. The development of such desirable error estimators turns out to be a quite dif®cult task. Virtually all (there are exceptions) error estimators in use are global in structure. For example, the element CCC 0271±2091/98/010033±11 $17.50 Received May 1996 # 1998 John Wiley & Sons, Ltd. * Correspondence to: J. T. Oden, Texas Institute for Computational and Applied Mathematics (TICAM), 3500 W Balcones Ctr Dr, MCC 3 11040, Austin, TX 7875, U.S.A. Contract grant sponsor: Of®ce of Naval Research; Contract grant number: N00014-89-J-3109