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Abstract The Simulating eXtreme Spacetimes Collaboration's code \texttt{SpEC} can now routinely simulate binary black hole mergers undergoing $$\sim25$$ orbits, with the longest simulations undergoing nearly $$\sim180$$ orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $$\mathcal{O}(10^{-1})$$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $$\mathcal{O}(10^{-4})$$, despite the resolutions being similar to the long simulations'. In this note, we explain why mismatch alone gives an incomplete picture of code---and waveform---quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $$\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$$ orbits. We argue that to ready the GW community for the sensitivity of future detectors, numerical relativity groups must be aware of this caveat, and also run future simulations with at least three resolutions to properly assess waveform accuracy. 

Abstract We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.