**Volume Title** ASP Conference Series, Vol. **Volume Number** **Author** c©**Copyright Year* * Astronomical Society of the Pacific An ADER-WENO Finite Volume AMR code for Astrophysics

Abstract. A high order one-step ADER-WENO finite volume scheme with Adap-tive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO re-construction. Thanks to the one-step nature of the underlying scheme, the resulting al-gorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the clas-sical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios. 1