Optimal Error Estimates of the Semidiscrete Central Discontinuous Galerkin Methods for Linear Hyperbolic Equations

DOI10.1137/16M1089484zbMath1383.65108MaRDI QIDQ4605272

Chi-Wang Shu, Yong Liu, Mengping Zhang

Publication date: 22 February 2018

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

zbMATH Keywords

numerical experimentsdiscontinuous Galerkin methodsuperconvergencesemidiscrete schemeoptimal error estimatelinear conservation laws

Mathematics Subject Classification ID

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) First-order hyperbolic equations (35L02)

Related Items (9)

Sub-Optimal Convergence of Discontinuous Galerkin Methods with Central Fluxes for Linear Hyperbolic Equations with Even Degree Polynomial Approximations ⋮ On generalized Gauss-Radau projections and optimal error estimates of upwind-biased DG methods for the linear advection equation on special simplex meshes ⋮ Optimal error estimates of the semidiscrete discontinuous Galerkin methods for two dimensional hyperbolic equations on Cartesian meshes using P^k elements ⋮ Optimal convergence and superconvergence of semi-Lagrangian discontinuous Galerkin methods for linear convection equations in one space dimension ⋮ Central Discontinuous Galerkin Methods for the Generalized Korteweg-de Vries Equation ⋮ Non-uniform L1/discontinuous Galerkin approximation for the time-fractional convection equation with weak regular solution ⋮ Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations ⋮ Central discontinuous Galerkin methods on overlapping meshes for wave equations ⋮ Optimal error estimates to smooth solutions of the central discontinuous Galerkin methods for nonlinear scalar conservation laws

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