Superconvergence of a WG method for the Stokes equations with continuous pressure.

In this paper, a new stabilizer free weak Galerkin finite element method with continuous finite element approximation of the pressure is proposed and analyzed for the Stokes problem. To achieve the same accuracy of the pressure approximation, the new method has less degrees of freedom among all existing weak Galerkin methods for the Stokes problem. Another feature of the new method is the superclose property for the approximation of the velocity. Error estimates for velocity in both the energy norm and L 2 norm and the estimate for pressure in L 2 norm are established. A local postprocessing technique is presented to obtain global superconvergence result. Numerical examples are shown to verify the theoretical results. [ABSTRACT FROM AUTHOR]