Geometry effects in nodal discontinuous Galerkin methods on curved elements that are provably stable

DOI10.1016/j.amc.2015.08.047zbMath1410.65372OpenAlexW1416087805MaRDI QIDQ668365

Gregor J. Gassner, David A. Kopriva

Publication date: 19 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.08.047

zbMATH Keywords

curved elementsenergy stabilityskew-symmetrydiscontinuous Galerkin spectral element methodGauss-Lobatto Legendremetric-identities

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (14)

An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. I: Theory and numerical verification ⋮ A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media ⋮ The BR1 scheme is stable for the compressible Navier-Stokes equations ⋮ A provably stable discontinuous Galerkin spectral element approximation for moving hexahedral meshes ⋮ Stability of overintegration methods for nodal discontinuous Galerkin spectral element methods ⋮ The discontinuous Galerkin method: derivation and properties ⋮ High-performance implementation of discontinuous Galerkin methods with application in fluid flow ⋮ Editorial: Preface to the special issue ``Recent advances in numerical methods for hyperbolic partial differential equations ⋮ An energy conservative \(hp\)-method for Liouville's equation of geometrical optics ⋮ Stability of discontinuous Galerkin spectral element schemes for wave propagation when the coefficient matrices have jumps ⋮ A split-form, stable CG/DG-SEM for wave propagation modeled by linear hyperbolic systems ⋮ Free-stream preservation for curved geometrically non-conforming discontinuous Galerkin spectral elements ⋮ Efficient Entropy Stable Gauss Collocation Methods ⋮ Skew-symmetric entropy stable modal discontinuous Galerkin formulations

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