Hyperbolic partial differential equations (PDEs) govern many processes in various application fields. ADER-DG is one type of numerical solver for such PDEs. This thesis aims to assess the quality of the ADER-DG solver in the context of tsunami simulations. The so-called shallow water equations (SWE) describe such tsunami scenarios. The simulations are generated with the newly developed SWE API, which offers a straightforward configuration of shallow water scenarios. The SWE API is built on top of the ExaHyPE 2 engine for solving hyperbolic PDEs, which, in turn, is an extension of the Peano 4 framework. Peano 4 offers a parallelized, efficient traversal of the simulation space, the means to store data in that space, and the ability to specify the processing stack for the data. The experiments in this thesis show that while ADER-DG has the potential to produce high-quality results, the simulations are unstable in dry regions. Conveniently, the SWE API is built in an easily extensible way, so implementing future approaches on that topic is straightforward.