We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)
methods. The output of this detector is a reliably scaled, element-wise smoothness
estimate which is suited as a control input to a shock capture mechanism. Using an
artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution
of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we
thoroughly justify the detector’s design and analyze its performance on a number of
benchmark problems. We further explain the scaling and smoothing steps necessary to turn
the output of the detector into a local, artificial viscosity. We close by providing an
extensive array of numerical tests of the detector in use.