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

  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},
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
Highly Influential
This paper has highly influenced 10 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
49 Citations
40 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 49 extracted citations


Publications referenced by this paper.
Showing 1-10 of 40 references

An introduction to the discontinuous galerkin method for convection-dominated problems, advanced numerical approximation of nonlinear hyperbolic equations (cetraro

  • B. Cockburn
  • Lecture Notes in Math., Springer, Berlin.,
  • 1997
Highly Influential
5 Excerpts

Parallel, adaptive finite element methods for conservation

  • R. Biswas, K. Devine, J. Flaherty
  • laws, Appl. Numer. Math.,
  • 1994
Highly Influential
5 Excerpts

Efficient implementation of essentially non-oscillatory shock-capturing schemes

  • C.-W. Shu, S. Osher
  • J. Comput. Phys.,
  • 1988
Highly Influential
6 Excerpts

Towards the ultimate conservative difference scheme I

  • B. van Leer
  • Lecture Notes in Phys.,
  • 1973
Highly Influential
14 Excerpts

Similar Papers

Loading similar papers…