## Scientific Computing and Numerics (SCAN) Seminar

Conservative finite difference and finite volume methods have proven extremely robust and reliable for magnetohydrodynamics simulations of binary neutron star mergers, core collapse supernova, and accretion onto a black hole. However, finite difference methods are generally less accurate and efficient than spectral methods when the solution is smooth, e.g. away from the stellar surfaces and shocks. The attractiveness of spectral methods has been demonstrated by thousands of long and highly accurate binary black hole simulations. 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 a discontinuous Galerkin-finite-difference hybrid method that inherits the best properties of both spectral and finite difference methods.