Journal of Scientific Computing

, Volume 44, Issue 2, pp 136–155 | Cite as

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

  • David A. KoprivaEmail author
  • Gregor Gassner
Original Research


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 are used to approximate the solutions and fluxes within the elements. Numerical experiments confirm the equivalence of the approximations and indicate that using Gauss quadrature with integration by parts once is the most efficient of the four approximations.


Spectral element Discontinuous Galerkin Collocation 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe Florida State UniversityTallahasseeUSA
  2. 2.Institute for Aerodynamics and GasdynamicsUniversity of StuttgartStuttgartGermany

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