This thesis focuses on the implementation and validation of coupled ADER-DG (Arbitrary higher order DERivative Discontinuous Galerkin) solvers within the ExaHyPE 2 framework for simulating elements of complex natural phenomena. By leveraging Lagrange interpolation and variable polynomial orders of the ADER-DG scheme, the coupled solvers demonstrate expected accuracy in capturing phenomena characterized by discontinuities. Through qualitative validation on scenarios like elastic wave propagation with a point source and quantitative validation on scenarios including Elastic Planar Waves and Euler Gaussian bell, the successful implementation is demonstrated. Additionally, scenarios like Acoustic Planar Waves are utilized for exploration of potential performance improvements. This work emphasizes the significance of coupled ADER-DG solvers in accurately capturing shock characteristics inspired by the limiting ADER-DG solver, laying the groundwork for further advancements in this direction.