Central Discontinuous Galerkin Methods on Overlapping Cells with a Nonoscillatory Hierarchical Reconstruction

@article{Liu2007CentralDG,
  title={Central Discontinuous Galerkin Methods on Overlapping Cells with a Nonoscillatory Hierarchical Reconstruction},
  author={Yingjie Liu and Chi-Wang Shu and Eitan Tadmor and Mengping Zhang},
  journal={SIAM J. Numerical Analysis},
  year={2007},
  volume={45},
  pages={2442-2467}
}
The central scheme of Nessyahu and Tadmor [J. Comput. Phys, 87 (1990)] solves hyperbolic conservation laws on a staggered mesh and avoids solving Riemann problems across cell boundaries. To overcome the difficulty of excessive numerical dissipation for small time steps, the recent work of Kurganov and Tadmor [J. Comput. Phys, 160 (2000)] employs a variable control volume, which in turn yields a semi-discrete non-staggered central scheme. Another approach, which we advocate here, is to view the… CONTINUE READING
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