Comparison of shock capturing schemes for the discontinuous Galerkin method in GRMHD

Using our open-source code SpECTRE, we present a detailed comparison of various limiting and shock capturing strategies for the discontinuous Galerkin methods proposed in the literature applied to a set of test problems in general relativistic magnetohydrodynamics (GRMHD). We compare the standard minmod/ΛΠN limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite difference hybrid method. The goal is to evaluate the robustness and accuracy of the different strategies in order to understand which are most likely able to simulate neutron stars.