A staggered discontinuous Galerkin method for the Stokes problem on rectangular meshes

In this paper, staggered discontinuous Galerkin (SDG) approximation for the Stokes problem is developed in a 2D square domain. The square domain is discretized by using rectangular meshes, which allow us easy identification of elements and hence a simple implementation of the SDG methods. By introducing proper function spaces and interpolations for the velocity vector field, its gradient, and the pressure, some required inf-sup conditions of our SDG method are shown. Then, thanks to the inf-sup conditions, the optimal convergence of our SDG approximation to the Stokes solution is obtained with respect to the polynomial order. Numerical results are included as well to validate the performance of our proposed SDG method for the Stokes problem.