Accuracy of High Order and Spectral Methods for Hyperbolic Conservation Laws with Discontinuous Solutions

DOI10.1137/140992758zbMath1317.65211OpenAlexW1509082886MaRDI QIDQ5499978

Jens Zudrop, Jan S. Hesthaven

Publication date: 5 August 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://infoscience.epfl.ch/record/202637

zbMATH Keywords

spectral methodshyperbolic conservation lawdiscontinuous GalerkinGibbs oscillations

Mathematics Subject Classification ID

Spectral methods applied to problems in fluid mechanics (76M22) Finite element methods applied to problems in fluid mechanics (76M10) 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)

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Adaptive modal filters based on artificial and spectral viscosity techniques, A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation

Cites Work

• Robust reprojection methods for the resolution of the Gibbs phenomenon
• Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• Family of spectral filters for discontinuous problems
• Numerical study of pseudospectral methods in shock wave applications
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function
• A note on the accuracy of spectral method applied to nonlinear conservation laws
• Stability of Pseudospectral and Finite-Difference Methods for Variable Coefficient Problems
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Convergence of Spectral Methods for Nonlinear Conservation Laws
• On a Cell Entropy Inequality for Discontinuous Galerkin Methods
• Legendre Pseudospectral Viscosity Method for Nonlinear Conservation Laws
• On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a Sub-Interval From a Spectral Partial Sum of a Pecewise Analytic Function
• Spectral Methods
• Filters, mollifiers and the computation of the Gibbs phenomenon
• Spectral Methods
• Spectral methods for hyperbolic problems
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