An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws

DOI10.1137/20M1354192zbMath1467.65095OpenAlexW3160041104WikidataQ115525528 ScholiaQ115525528MaRDI QIDQ4989949

Chi-Wang Shu, Yong Liu, Jianfang Lu

Publication date: 27 May 2021

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

Full work available at URL: https://doi.org/10.1137/20m1354192

zbMATH Keywords

boundednesssuperconvergencehyperbolic conservation lawsoptimal error estimatesconservationdiscontinuous Galerkin

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

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• Entropy viscosity method for nonlinear conservation laws
• Insights from von Neumann analysis of high-order flux reconstruction schemes
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• The piecewise parabolic method (PPM) for gas-dynamical simulations
• Numerical solutions of partial differential equations
• On maximum-principle-satisfying high order schemes for scalar conservation laws
• High resolution schemes for hyperbolic conservation laws
• Uniformly high order accurate essentially non-oscillatory schemes. III
• 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
• Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
• Local discontinuous Galerkin methods for partial differential equations with higher order derivatives
• Superconvergence of local discontinuous Galerkin methods for partial differential equations with higher order derivatives
• Efficient implementation of weighted ENO schemes
• Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• Entropy stable shock capturing space-time discontinuous Galerkin schemes for systems of conservation laws
• Basic principles of mixed Virtual Element Methods
• Superconvergence of the direct discontinuous Galerkin method for convection-diffusion equations
• Superconvergence of Discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• Superconvergence of discontinuous Galerkin methods for 1-D linear hyperbolic equations with degenerate variable coefficients
• 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
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations
• Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
• Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
• Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation
• Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using P^k elements
• Superconvergence of Discontinuous Galerkin Methods for Linear Hyperbolic Equations
• Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation
• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
• Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method