  We present a sub-cell accurate shock-fitting technique using a high-order
extended discontinuous Galerkin (XDG) method, where a computational cell of the
background grid is cut into two cut-cells at the shock position. Our technique
makes use of a sharp interface description where the shock front is implicitly
defined by means of the zero iso-contour of a level-set function. A novel
implicit pseudo-time-stepping procedure is employed to correct the position of
the shock front inside the cut background cell by using cell-local indicators,
since the position and shape of shock waves are not known a priori for the
general, multi-dimensional case. This iterative correction terminates if the
shock front has converged to the exact position. The procedure is demonstrated
for the test case of a one-dimensional stationary normal shock wave.
Furthermore, the underlying sharp interface approach drastically reduces the
complexity of the grid handling, since a simple Cartesian background grid can
be employed.
