High order entropy preserving ADER-DG schemes

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain desired result, equip the space part of method with correction terms that balance production in space, inspired by work Abgrall. Whereas for time-discretization apply relaxation approach introduced Ketcheson allows to modify timestep preserve machine precision. Up our knowledge, it is first time provable ADER-DG scheme constructed. We verify theoretical results various numerical simulations.