Optimal error estimate and superconvergence of the DG method for first-order hyperbolic problems

DOI10.1016/j.cam.2010.05.023zbMath1205.65253OpenAlexW1977403288MaRDI QIDQ711237

Tie Zhang, Zheng Li

Publication date: 25 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.cam.2010.05.023

zbMATH Keywords

discontinuous Galerkin methodsuperconvergenceerror estimatefirst order hyperbolic equation

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) Initial-boundary value problems for first-order hyperbolic equations (35L04)

Related Items (4)

A posteriori error analysis of the discontinuous Galerkin method for two-dimensional linear hyperbolic conservation laws on Cartesian grids ⋮ A Recovery-Based Error Estimator for the Discontinuous Galerkin Method for Transient Linear Hyperbolic Conservation Laws on Cartesian Grids ⋮ Superconvergence and \textit{a posteriori} error estimates of the DG method for scalar hyperbolic problems on Cartesian grids ⋮ Hybrid Fourier pseudospectral/discontinuous Galerkin time-domain method for wave propagation

Cites Work

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• Symmetric positive linear differential equations
• A Note on the Convergence of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes
• An Optimal-Order Error Estimate for the Discontinuous Galerkin Method
• DISCONTINUOUS GALERKIN METHODS FOR FIRST-ORDER HYPERBOLIC PROBLEMS
• An Analysis of the Discontinuous Galerkin Method for a Scalar Hyperbolic Equation
• L₂ is a continuable initial condition for kreiss' mixed problems

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