Residual-based stabilized higher-order fem for a generalized Oseen problem

In many numerical schemes for standard turbulence models for the nonstationary, incompressible Navier-Stokes equations, the problem is split into linearized auxiliary problems of advection-diffusion-reaction and of Oseen type. Here we present the numerical analysis of a conforming hp-version for stabilized Galerkin methods of SUPG/PSPG-type of the latter problem whereas the analysis of the former problem is reviewed in Ref. 22. We prove a modified inf-sup condition with a constant, which is independent of the spectral order and the viscosity. Moreover, the analysis of the stabilization parameters highlights the role of grad-div stabilization, in particular in case of div-stable velocity-pressure approximation.