ADER Shock-Capturing Methods and Geophysical Applications

This paper deals with a new generation of shock-capturing methods of the Godunov-type, called ADER methods. These, are based on the solution of the Derivative Riemann Problem (DRP), whose initial conditions are piece-wise smooth functions, rather than piece-wise constant, as in the classical Godunov method. The resulting numerical methods are constructed in the frame of finite volumes and discontinuous Galerkin finite element methods, and are of arbitrary order of accuracy in space and time, on both structured and unstructured meshes. There are many applications in which the use of such methods is essential, both in terms of solution accuracy and efficiency. Examples include acoustics and general wave propagation problems involving long time evolution. Here we illustrate the applicability of the proposed methods by solving some geophysical problems.

@inproceedings{id594,
  address = {Bangalore},
  author = {Toro, E. and K\"aser, M. and Dumbser, M. and Castro, C.},
  booktitle = {Proceedings of the 25th International Symposium on Shock Waves - ISSW25},
  language = {en},
  title = {ADER Shock-Capturing Methods and Geophysical Applications},
  year = {2005},
}

%O Conference Proceedings
%C Bangalore
%A Toro, E.
%A Käser, M.
%A Dumbser, M.
%A Castro, C.
%B Proceedings of the 25th International Symposium on Shock Waves - ISSW25
%G en
%T ADER Shock-Capturing Methods and Geophysical Applications
%D 2005