We present results of thorough benchmarking of an arbitrary high-order derivative discontinuous Galerkin (ADER-DG) method on unstructured meshes for advanced earthquake dynamic rupture problems. We verify the method by comparison to well-established numerical methods in a series of verification exercises, including dipping and branching fault geometries, heterogeneous initial conditions, bimaterial interfaces and several rate-and-state friction laws. We show that the combination of meshing flexibility and high-order accuracy of the ADER-DG method makes it a competitive tool to study earthquake dynamics in geometrically complicated setups.