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High order numerical methods

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High order numerical methods

Computational time vs. L1 error, different orders k
Low orders are much more diffusive

Working group: R.Borsche, J. Kall, F. Schneider

Cooperations: G. Alldredge (Aachen)

Funding: Center for Mathematical and Computational Modelling (CMCM)

This research aims at finding high order numerical methods for (partial) differential equations. In general, high order methods allow a very efficient solution of smooth problems. Even though the computational effort given a fixed grid is usually increasing with the approximation order, the effort to achieve a given error tolerance with a lower order scheme on a finer grid is typically much higher.

We investigate different types of high order schemes:

  • Finite volume schemes using reconstruction techniques (e.g. WENO reconstruction)
  • Evolution methods (e.g. Discontinuous Galerkin method)

More information and Matlab scripts can be found in the corresponding subsections.