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

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