Alternating Evolution Schemes for Hamilton-Jacobi Equations

@article{Liu2013AlternatingES,
  title={Alternating Evolution Schemes for Hamilton-Jacobi Equations},
  author={Hailiang Liu and Michael Pollack and Haseena Saran},
  journal={SIAM J. Sci. Comput.},
  year={2013},
  volume={35}
}
In this work, we propose a high-resolution alternating evolution (AE) scheme to solve Hamilton--Jacobi equations. The construction of the AE scheme is based on an alternating evolution system of the Hamilton--Jacobi equation, following the idea previously developed for hyperbolic conservation laws. A semidiscrete scheme derives directly from a sampling of this system on alternating grids. Higher order accuracy is achieved by a combination of high order nonoscillatory polynomial reconstruction… 
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