Exponential convergence of mixed hp-DGFEM for Stokes flow in polygons

Over the last few years, several mixed discontinuous Galerkin finite element methods (DGFEM) have been proposed for the discretization of incompressible fluid flow problems. We mention here only the piecewise solenoidal discontinuous Galerkin methods introduced in [5,25], the local discontinuous Galerkin methods of [12,11], and the interior penalty methods studied in [24,33,18]. Some of the main motivations that led to the above methods are the following: First of all, the discontinuous nature of the finite element spaces allows one to easily treat convective terms by suitable upwind fluxes, similarly to the original discontinuous Galerkin discretizations of (non-linear) hyperbolic equations (see [13,10,14] and the references therein). Thus,