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The incompressible Navier-Stokes equations are solved in a channel, using aDiscontinuous Galerkin method over staggered grids. The resulting linearsystems are studied both in terms of the structure and in terms of the spectralfeatures of the related coefficient matrices. In fact, the resulting matricesare of block type, each block showing Toeplitz-like, band, and tensor structureat the same time. Using this rich matrix-theoretic information and theToeplitz, Generalized Locally Toeplitz technology, a quite complete spectralanalysis is presented, with the target of designing and analyzing fastiterative solvers for the associated large linear systems. Quite promisingnumerical results are presented, commented, and critically discussed forelongated two- and three-dimensional geometries.

A matrix-theoretic spectral analysis of incompressible Navier-Stokes staggered DG approximation and related solvers