Stabilized hp-DGFEM for Incompressible Flow

Source abstract

We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that ℚ k -ℚ k and ℚ k -ℚ k-1 elements satisfy a generalized inf–sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, edges, and corners. The discrete inf–sup constant is proven to be independent of the aspect ratios of the anisotropic elements and to decrease as k -1/2 with the approximation order. We also show that the generalized inf–sup condition leads to a global stability result in a suitable energy norm.