Local derivative post-processing for the discontinuous Galerkin method

DOI10.1016/j.jcp.2009.08.017zbMath1176.65108OpenAlexW2019723871MaRDI QIDQ1038033

Jennifer K. Ryan, Bernardo Cockburn

Publication date: 17 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2009.08.017

zbMATH Keywords

discontinuous Galerkin methodhyperbolic equationspost-processingaccuracy enhancement

Mathematics Subject Classification ID

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

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Cites Work

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• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• On a one-sided post-processing technique for the discontinuous Galerkin methods
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• Postprocessing for the Discontinuous Galerkin Method over Nonuniform Meshes
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Higher Order Local Accuracy by Averaging in the Finite Element Method
• High Order Local Approximations to Derivatives in the Finite Element Method
• Total variation diminishing Runge-Kutta schemes
• Extension of a Post Processing Technique for the Discontinuous Galerkin Method for Hyperbolic Equations with Application to an Aeroacoustic Problem
• Enhanced accuracy by post-processing for finite element methods for hyperbolic equations