Analysis of an SDG Method for the Incompressible Navier-Stokes Equations

In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier--Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.