Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

@article{Xing2013PositivityPreservingWD,
  title={Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes},
  author={Yulong Xing and Xiangxiong Zhang},
  journal={Journal of Scientific Computing},
  year={2013},
  volume={57},
  pages={19-41}
}
The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In “Xing et al. Adv. Water Resourc. 33: 1476–1493, 2010)”, the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. In this paper, we… 
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