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Abstract

Discontinuous Galerkin methods are popular because they can achieve high
order where the solution is smooth, because they can capture shocks while
needing only nearest-neighbor communication, and because they are relatively
easy to formulate on complex meshes. We perform a detailed comparison of
various limiting strategies presented in the literature applied to the
equations of general relativistic magnetohydrodynamics. We compare the standard
minmod/$\Lambda\Pi^N$ limiter, the hierarchical limiter of Krivodonova, the
simple WENO limiter, the HWENO limiter, and a discontinuous
Galerkin-finite-difference hybrid method. The ultimate goal is to understand
what limiting strategies are able to robustly simulate magnetized TOV stars
without any fine-tuning of parameters. Among the limiters explored here, the
only limiting strategy we can endorse is a discontinuous
Galerkin-finite-difference hybrid method.