The Derivative Riemann Problem: The Basis for High Order ADER Schemes

The corner stone of arbitrary high order schemes (ADER schemes) is the solution of the derivative Riemann problem at the element interfaces, a generalization of the classical Riemann problem first used by Godunov in 1959 to construct a first-order upwind numerical method for hyperbolic systems. The derivative Riemann problem extends the possible initial conditions to piecewise smooth functions, separated by a discontinuity at the interface. In the finite volume framework, these piecewise smooth functions are obtained from cell averages by a high order non-oscillatoryWENO reconstruction, allowing hence the construction of non-oscillatory methods with uniform high order of accuracy in space and time.

@inproceedings{id602,
  address = {Delft},
  author = {Toro, E. and Dumbser, M. and Titarev, V. and K\"aser, M.},
  booktitle = {Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS},
  language = {en},
  title = {The Derivative Riemann Problem: The Basis for High Order ADER Schemes},
  year = {2006},
}

%O Conference Proceedings
%C Delft
%A Toro, E.
%A Dumbser, M.
%A Titarev, V.
%A Käser, M.
%B Proceedings of the European Conference on Computational Fluid Dynamics, ECCOMAS
%G en
%T The Derivative Riemann Problem: The Basis for High Order ADER Schemes
%D 2006