  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 divergence preserving velocity
reconstruction operator, which is the crux for pressure independent velocity
error estimates. The optimal convergence for velocity gradient, velocity and
pressure are proved. In addition, we are able to prove the superconvergence of
velocity approximation by the incorporation of divergence preserving velocity
reconstruction operator in the dual problem, which is also an important
contribution of this paper. Finally, several numerical experiments are carried
out to confirm the theoretical findings.
