Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws

DOI10.1051/m2an/2022037zbMath1497.65174OpenAlexW4223900446MaRDI QIDQ5867511

Mengjiao Jiao, Yan Jiang, Chi-Wang Shu, Mengping Zhang

Publication date: 14 September 2022

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

Full work available at URL: https://doi.org/10.1051/m2an/2022037

zbMATH Keywords

optimal error estimatesnonlinear conservation lawscentral DG method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
• Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
• Non-oscillatory central differencing for hyperbolic conservation laws
• Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• New central and central discontinuous Galerkin schemes on overlapping cells of unstructured grids for solving ideal magnetohydrodynamic equations with globally divergence-free magnetic field
• Central schemes on overlapping cells
• Operator bounds and time step conditions for the DG and central DG methods
• Central local discontinuous galerkin methods on overlapping cells for diffusion equations
• L²stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
• Finite Volume Methods for Hyperbolic Problems
• Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations
• Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
• Runge-Kutta Central Discontinuous Galerkin Methods for the Special Relativistic Hydrodynamics
• Central Discontinuous Galerkin Methods on Overlapping Cells with a Nonoscillatory Hierarchical Reconstruction
• Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
• A priorierror estimates to smooth solutions of the third order Runge–Kutta discontinuous Galerkin method for symmetrizable systems of conservation laws
• Error Estimates to Smooth Solutions of Runge–Kutta Discontinuous Galerkin Method for Symmetrizable Systems of Conservation Laws

This page was built for publication: Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws