ADER schemes for three-dimensional non-linear hyperbolic systems

352 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Godunov-type methods for free-surface shallow flows: A review (2007, background): “See also Dumbser (2005), Dumbser and Munz (2005), Käser (2003, 2004), Käser and Iske (2005), Takakura and Toro (2002), Titarev and Toro (2002, 2005) and Toro and Titarev (2005).”
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (2007, methodology): “This is described in more detail in [11,15,44,41,45] for the nonlinear case.”
Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws (2012, methodology): “6) is performed with strong stability preserving Runge–Kutta methods [11] or with ADER schemes [34].”
Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials (2012, methodology): “Several strategies became very popular due to their intrinsic simplicity such that the MUSCL method [3,6,7,20,26,32] or their efficiency to achieve very high-order accuracy such that the ENO/WENO method [1,21,29,30,36,37,46,18,19,35,49,41], the Discontinuous Galerkin method [9– 12], the ADER method ”