Convergence of second-order, entropy stable methods for multi-dimensional conservation laws

DOI10.1051/m2an/2019090zbMath1446.65088arXiv1906.05115OpenAlexW3036396377MaRDI QIDQ5118618

Neelabja Chatterjee, Ulrik Skre Fjordholm

Publication date: 26 August 2020

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05115

zbMATH Keywords

finite volume methodsentropy stabilitymulti-dimensional conservation lawsTECNO scheme

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Weak solutions to PDEs (35D30) Resonance in context of PDEs (35B34) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

On Thermodynamically Compatible Finite Volume Schemes for Continuum Mechanics, Convergence of entropy stable schemes for degenerate parabolic equations with a discontinuous convection term, On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows

Cites Work

• Unnamed Item
• Unnamed Item
• Handbook of numerical methods for hyperbolic problems. Basic and fundamental issues
• Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux
• Some results on uniformly high-order accurate essentially nonoscillatory schemes
• Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws
• The study on application way of the compensated compactness theory
• ENO reconstruction and ENO interpolation are stable
• Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws
• Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes
• Riemann Solvers, the Entropy Condition, and Difference
• The Numerical Viscosity of Entropy Stable Schemes for Systems of Conservation Laws. I
• On finite-difference approximations and entropy conditions for shocks
• Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
• Finite Volume Methods for Hyperbolic Problems
• High-order accurate, fully discrete entropy stable schemes for scalar conservation laws
• Fully Discrete, Entropy Conservative Schemes of ArbitraryOrder
• Error Estimates for Finite Volume Approximations of Classical Solutions for Nonlinear Systems of Hyperbolic Balance Laws
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Hyperbolic Conservation Laws in Continuum Physics
• Front tracking for hyperbolic conservation laws