Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments

By Xiangxiong Zhang, Chi-Wang Shu. Proceedings of the Royal Society A, 2011

395 citations recorded by the source corpus.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/1f4289543cb5dbf419fd7d01a2ff404ab1c54cfa

How researchers see this paper

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

In Atmospheric Science

1. Michael Dumbser
2. Raphaël Loubère
3. Steven Diot
4. Chi-Wang Shu
5. Yulong Xing
6. Olindo Zanotti
7. Mark H. Carpenter
8. Giacomo Dimarco

In Computational Mechanics

1. Chi-Wang Shu
2. Raphaël Loubère
3. Steven Diot
4. Michael Dumbser
5. Olindo Zanotti
6. Yulong Xing
7. Eleuterio F. Toro
8. Martin Käser

Citations in the corpus

• A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, background): “For the most recent developments in the field of DG schemes see, for example, [116, 113, 117].”
• A Survey of High Order Schemes for the Shallow Water Equations (2014, background): “As mentioned in [61, 68], for those points in SK, instead of requiring hK(x)≥ 0,∀x∈ SK, it suffices to require ∑x∈SK hK(x)wx≥ 0 to have positivity of h n+1 K .”