On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods

@article{Kopriva2010OnTQ,
  title={On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods},
  author={David A. Kopriva and Gregor Gassner},
  journal={J. Sci. Comput.},
  year={2010},
  volume={44},
  pages={136-155}
}
We examine four nodal versions of tensor product discontinuous Galerkin spectral element approximations to systems of conservation laws for quadrilateral or hexahedral meshes. They arise from the two choices of Gauss or Gauss-Lobatto quadrature and integrate by parts once (I) or twice (II) formulations of the discontinuous Galerkin method. We show that the two formulations are in fact algebraically equivalent with either Gauss or Gauss-Lobatto quadratures when global polynomial interpolations… CONTINUE READING
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