Journal of Scientific Computing

, Volume 27, Issue 1–3, pp 215–230 | Cite as

Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes

  • Michael Dumbser
  • Claus-Dieter Munz


In this article we propose the use of the ADER methodology of solving generalized Riemann problems to obtain a numerical flux, which is high order accurate in time, for being used in the Discontinuous Galerkin framework for hyperbolic conservation laws. This allows direct integration of the semi-discrete scheme in time and can be done for arbitrary order of accuracy in space and time. The resulting fully discrete scheme in time does not need more memory than an explicit first order Euler time-stepping scheme. This becomes possible because of an extensive use of the governing equations inside the numerical scheme itself via the so-called Cauchy–Kovalewski procedure. We give an efficient algorithm for this procedure for the special case of the nonlinear two-dimensional Euler equations. Numerical convergence results for the nonlinear Euler equations results up to 8th order of accuracy in space and time are shown


Discontinuous Galerkin finite elements ADER approach generalized riemann problems Cauchy–Kovalewski procedure 


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Copyright information

© Springer Science+Business Media Inc 2005

Authors and Affiliations

  1. 1.Institut für Aerodynamik und GasdynamikUniversity of StuttgartStuttgartGermany

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