The presence of discontinuities in nonlinear hyperbolic conservation laws is a long-standing challenge in the development of high-order numerical methods. In this talk, I will present an approach to shock capturing for discontinuous spectral element methods which uses invariant domain preservation techniques to construct a low-order scheme devoid of tunable parameters. This technique is then enhanced using a novel point-local entropy residual indicator that is independent of grid spacing and polynomial order, which enables the scheme to recover high-order accuracy in smooth regions and sub-element resolution of discontinuous solutions even at very high orders. The effectiveness of this method is then shown in several numerical test cases that include shock tubes, complex explosion problems, and aeronautical applications.