Resumen de Discontinuous Galerkin methods with Trefftz approximations

Fritz Kretzschmar, Sascha Schnepp, Igor Tsukerman, Thomas Weiland

• We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space�time Trefftz basis functions that satisfy the underlying partial differential equations and the respective interface boundary conditions exactly in an element-wise fashion. The basis functions can be of arbitrarily high order and we demonstrate spectral convergence in the space�time L2-norm. Therefore high order time integration is an inherent property of the method and clearly sets it apart from methods that employ a high order approximation in space only.