ADER-DG with a-posteriori finite-volume limiting to simulate tsunamis in a parallel adaptive mesh refinement framework. In this paper, we present the application of the ADER discontinuous Galerkin method with an -posteriori finite-volume limiter on the simulation of tsunamis. The goal is to obtain a method of high-order convergence in deep water areas while being able to handle wetting & drying at coast lines. Several adjustments of the original ADER-DG method are presented to preserve characteristics like the well-balanced property. We evaluate and confirm developed concepts by a series of numerical tests and present them in the context of reconstructed tsunamis.