Princeton University Computational Astrophysics Club

Conservative finite difference methods have proven extremely robust and reliable for magnetohydrodynamics simulations of binary neutron star mergers. However, finite difference methods are generally less accurate and efficient than spectral methods when the solution is smooth, for example everywhere outside the neutron stars. Thousands of long and highly accurate binary black hole merger simulations have been performed, demonstrating the attractiveness of spectral methods. Discontinuous Galerkin methods seek to provide the accuracy of spectral methods while also robustly capturing shocks in hydrodynamics simulations. I will give an overview of finite difference and discontinuous Galerkin methods and present a new hybrid method that demonstrably inherits the best properties of both finite difference/volume and spectral methods.