Superconvergence of Finite Element Approximations for the Stokes Problem by Projection Methods

Abstract

This paper derives a general superconvergence result for finite element approximations 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 regularity assumption for the Stokes problem and is applicable to any finite element method with regular but nonuniform partitions. The method is proved to give a convergent scheme for certain finite element spaces which fail to satisfy the well-known uniform inf-sup condition of Brezzi and Babuska.