Superconvergence analysis for the Navier–Stokes equations Original Research Article

This paper derives a general superconvergence result for finite element approximations of the Navier–Stokes problem by using a least-squares surface fitting method proposed and analyzed recently by Wang for the standard Galerkin method. The superconvergence result is based on some regularity assumption for the Navier–Stokes problem and is applicable to any finite element method with quasi-uniform meshes. The method is demonstrated to give a convergent scheme for finite element spaces which fail to satisfy the well-known uniform inf–sup condition of Brezzi and Babuška.