Florian J. Hindenlang, Gregor J. Gassner and Claus-Dieter Munz
The upper plot shows the boundary layer solution for a DG scheme of polynomial degree N = 4 on a stretched grid (line with symbols). We also plot the Jacobian of the elements J * . In the figure, we show the approximation error (u − uex), which is reduced by an order of magnitude when replacing the linear element mapping ( Ng = 1, constant Jacobian) by a high order mapping Ng > 1. This is due to the distributed resolution inside the grid cells, which is reflected in the smoothed Jacobian.