  The incompressible Navier-Stokes equations are solved in a channel, using a
Discontinuous Galerkin method over staggered grids. The resulting linear
systems are studied both in terms of the structure and in terms of the spectral
features of the related coefficient matrices. In fact, the resulting matrices
are of block type, each block showing Toeplitz-like, band, and tensor structure
at the same time. Using this rich matrix-theoretic information and the
Toeplitz, Generalized Locally Toeplitz technology, a quite complete spectral
analysis is presented, with the target of designing and analyzing fast
iterative solvers for the associated large linear systems. Quite promising
numerical results are presented, commented, and critically discussed for
elongated two- and three-dimensional geometries.
