  In this paper we propose a novel staggered discontinuous Galerkin method for
the Brinkman problem on general quadrilateral and polygonal meshes. The
proposed method is robust in the Stokes and Darcy limits, in addition, hanging
nodes can be automatically incorporated in the construction of the method,
which are desirable features in practical applications. There are three
unknowns involved in our formulation, namely velocity gradient, velocity and
pressure. Unlike the original staggered DG formulation proposed for the Stokes
equations in \cite{KimChung13}, we relax the tangential continuity of velocity
and enforce different staggered continuity properties for the three unknowns,
which is tailored to yield an optimal $L^2$ error estimates for velocity
gradient, velocity and pressure independent of the viscosity coefficient.
Moreover, by choosing suitable projection, superconvergence can be proved for
$L^2$ error of velocity. Finally, several numerical results illustrating the
good performances of the proposed method and confirming the theoretical
findings are presented.
