Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations

DOI10.4208/jcm.2002-m2019-0305zbMath1499.65507arXiv2001.03825OpenAlexW3164908915WikidataQ114021202 ScholiaQ114021202MaRDI QIDQ5079518

Mengping Zhang, Chi-Wang Shu, Yong Liu

Publication date: 27 May 2022

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

Full work available at URL: https://arxiv.org/abs/2001.03825

zbMATH Keywords

discontinuous Galerkin methodcentral fluxsub-optimal convergence rates

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators (35L85)

Related Items

Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems, A Conservative and Energy Stable Discontinuous Spectral Element Method for the Shifted Wave Equation in Second Order Form, On generalized Gauss-Radau projections and optimal error estimates of upwind-biased DG methods for the linear advection equation on special simplex meshes

Cites Work

• Unnamed Item
• Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media
• Sub-optimal convergence of non-symmetric discontinuous Galerkin methods for odd polynomial approximations
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Stability analysis and error estimates of local discontinuous Galerkin methods for convection-diffusion equations on overlapping meshes
• Optimal energy-conserving discontinuous Galerkin methods for linear symmetric hyperbolic systems
• Strong Stability-Preserving High-Order Time Discretization Methods
• Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations
• $L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations
• Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation
• Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
• Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations
• Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using P^k elements
• Effective Computational Methods for Wave Propagation