An extended Discontinuous Galerkin and Spectral Difference Method with modal filtering

DOI10.1002/zamm.201200051zbMath1275.65062OpenAlexW2084432980MaRDI QIDQ2863156

Thomas Sonar, Martina Wirz, Andreas Meister, Sigrun Ortleb

Publication date: 21 November 2013

Published in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/zamm.201200051

zbMATH Keywords

triangulationshyperbolic conservation lawsdiscontinuitiesspectral differencemodal filtersdiscontinuous galerkinPKD polynomials

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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 (5)

Generalised summation-by-parts operators and variable coefficients ⋮ Application of modal filtering to a spectral difference method ⋮ Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators ⋮ Smooth and compactly supported viscous sub-cell shock capturing for discontinuous Galerkin methods ⋮ Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points

Cites Work

• On the stability and accuracy of the spectral difference method
• Spectral methods on triangles and other domains
• Detection of edges in spectral data
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Spectral difference method for unstructured grids. I. Basic formulation
• Spectral difference method for unstructured grids. II. Extension to the Euler equations
• A Lobatto interpolation grid over the triangle

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