A pressure robust staggered discontinuous Galerkin method for the Stokes equations

In this paper, we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right-hand side of the body force in the discrete formulation by exploiting a divergence preserving velocity reconstruction operator, which is the crux for pressure-independent velocity error estimates. The optimal convergence for the velocity gradient, velocity, and pressure is proved. In addition, we can establish the superconvergence of the velocity approximation by incorporating a divergence preserving velocity reconstruction operator in the dual problem, which is also an essential contribution of this paper. Finally, several numerical experiments are carried out to confirm the theoretical findings.