Superconvergence of finite element approximations for the Stokes problem by projection methods

This paper derives a general superconvergence result for finite element app roximations of the Stokes problem by using projection methods proposed and analyzed recently by Wang [J. Math. Study, 33 (2000), pp. 229-243] for the standard Galerkin method. The superconvergence result is based on some regu larity assumption for the Stokes problem and is applicable to any finite el ement method with regular but nonuniform partitions. The method is proved t o give a convergent scheme for certain finite element spaces which fail to satisfy the well-known uniform inf-sup condition of Brezzi and Babuska.