Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: \( h p\) version

DOI10.1016/j.camwa.2020.01.017zbMath1446.65109OpenAlexW3004620671MaRDI QIDQ2192501

Jiangxing Wang, Yu Du

Publication date: 17 August 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.01.017

zbMATH Keywords

wave equationdiscontinuous Galerkin methodenergy conserving method\( hp\) error estimate

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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)

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Uses Software

• DG_DATH_ELASTIC_V1.0

Cites Work

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• A New Discontinuous Galerkin Formulation for Wave Equations in Second-Order Form
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• The $h-p$ version of the finite element method with quasiuniform meshes
• Convergence Analysis of a Discontinuous Galerkin Method for Wave Equations in Second-Order Form
• The Optimal Convergence of theh‐pVersion of the Finite Element Method with Quasi‐Uniform Meshes
• The Mathematical Theory of Finite Element Methods
• Approximation Theory for the p-Version of the Finite Element Method in Three Dimensions. Part 1: Approximabilities of Singular Functions in the Framework of the Jacobi-Weighted Besov and Sobolev Spaces

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