Third order nonoscillatory central scheme for hyperbolic conservation laws

@article{Liu1998ThirdON,
  title={Third order nonoscillatory central scheme for hyperbolic conservation laws},
  author={Xu-Dong Liu and Eitan Tadmor},
  journal={Numerische Mathematik},
  year={1998},
  volume={79},
  pages={397-425}
}
Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and… 

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