I'm trying to define a "spectral sensor" and see if that can help identifying a shock vs smooth flow. Instead of only looking at s_p = ||q_{p-1}-q_p|| / ||q_p||, I look at s_i for i = 0,...,n, such that \Sum_{i} s_i = 1. The idea is that the error (i.e. s_i) should decay exponentially fast at shocks and slower everywhere else. I've tested that on a couple of test cases so far and haven't seen anything. But I was using p=4 and p=5 and I wonder if this behaviour only appears at even higher order.