A comparison of the discontinuous-Galerkin- and spectral-difference-method on triangulations using PKD polynomials

DOI10.1016/j.jcp.2012.07.025zbMath1257.65054OpenAlexW1999986220MaRDI QIDQ695147

Thomas Sonar, Martina Wirz, Sigrun Ortleb, Andreas Meister

Publication date: 20 December 2012

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2012.07.025

zbMATH Keywords

comparison of methodsnumerical examplesdiscontinuous Galerkin methodhyperbolic conservation lawsspectral difference methodProvid-Koornwinder-Dubiner (PKD) polynomials

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (3)

A stable spectral difference approach for computations with triangular and hybrid grids up to the \(6^{th}\) order of accuracy ⋮ Generalised summation-by-parts operators and variable coefficients ⋮ On the accuracy and efficiency of discontinuous Galerkin, spectral difference and correction procedure via reconstruction methods

Cites Work

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• On the stability and accuracy of the spectral difference method
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• Spectral methods on triangles and other domains
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• A conservative staggered-grid Chebyshev multidomain method for compressible flows
• Spectral difference method for unstructured grids. I. Basic formulation
• Spectral difference method for unstructured grids. II. Extension to the Euler equations
• Adaptive Spectral Filtering and Digital Total Variation Postprocessing for the DG Method on Triangular Grids: Application to the Euler Equations
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• A Lobatto interpolation grid over the triangle
• Spectral/hp Element Methods for Computational Fluid Dynamics

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