A discontinuous Galerkin method for convection-dominated compressible viscous Navier-Stokes equations with an inflow boundary condition

Abstract

A linearized steady-state compressible viscous Navier Stokes system with an in ow boundary condition is considered. A discontinuous Galerkin method for this system is formulated with convection-dominance and O(h) viscous functions where h is the mesh size in a given triangulation. The resulting finite element method is explicit and valid for all polynomials of degree greater than or equal to 1. We show a L-p-stability and derive error estimates for velocity and pressure, respectively. I particular, the compressibility number kappa := rho'/rho is regarded as essential in showing our stability results.