To stabilize our high order Discontinuous Galerkin discretization, a artificial viscosity approach introduced by Persson and Peraire is used and adopted to the local time stepping scheme. To highlight the potential of this new artificial viscosity approach, the famous double Mach reflection example of Woodward and Collela is considered. The characteristic part of this solution is the double Mach stem region and the shear layer instability. We compare our Discontinuous Galerkin results with state of the art 5th order accurate WENO Finite Volume solutions with different spatial resolutions. Due to the subcell resolution of the Discontinuous Galerkin approach with polynomial degree N=4, four times the number of grid cells are needed for the WENO Finite Volume approximation to match the Discontinuous Galerkin result.