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

Authors:
David A. Kopriva;Gregor Gassner
Affiliations:
Department of Mathematics, The Florida State University, Tallahassee, USA 32312;Institute for Aerodynamics and Gasdynamics, University of Stuttgart, Stuttgart, Germany 70550
Venue:
Journal of Scientific Computing
Year:
2010

Citing 12
Cited 5

Approximate Riemann solvers, parameter vectors, and difference schemes

Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Spectral element approximation of convection—diffusion type problems

Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
An efficient implicit discontinuous spectral Galerkin method

Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

Journal of Computational Physics
De-aliasing on non-uniform grids: algorithms and applications

Journal of Computational Physics
Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes

Journal of Scientific Computing
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)

Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Numerical simulation of optical coupling and light propagation in coupled optical resonators with size disorder

Applied Numerical Mathematics
A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

Journal of Computational Physics
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers

Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers
A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Modeling

SIAM Journal on Scientific Computing

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

Journal of Computational Physics
A Comparison of the Dispersion and Dissipation Errors of Gauss and Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods

SIAM Journal on Scientific Computing
A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes

Journal of Computational Physics
On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods

Journal of Computational Physics
ALE-DGSEM approximation of wave reflection and transmission from a moving medium

Journal of Computational Physics

Quantified Score

Hi-index	0.02

Visualization

Abstract

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.