Department of Mechanics: Seminar: Abstract Kretzschmar

The Discontinuous Galerkin Trefftz Method

In the recent year we have developed a novel type of Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space–time Trefftz-type basis functions that satisfy the underlying partial differential equations exactly in an element–wise fashion. In the present talk we show the current status of our effort to extend the recently developed (1+1)-dimensional Discontinuous Galerkin Trefftz Finite Element Method to (3+1)-dimensions. One suitable choice of such basis functions are plane waves traveling in various directions that are expressed as space-time polynomials of arbitrarily high order p. Methods implying such basis sets can exhibit spectral convergence under p enrichment in the whole space–time domain of interest. Formulating the approximation in terms of a space–time Trefftz basis makes high order time integration an inherent property of the method and clearly sets it apart from methods which employ a high order approximation in space only.