On the accuracy of the discontinuous Galerkin method in calculation of shock waves

DOI10.1134/S0965542518080122zbMath1412.76056OpenAlexW2892832031MaRDI QIDQ1755616

O. A. Neklyudova, V. V. Ostapenko, M. E. Ladonkina, V. F. Tishkin

Publication date: 10 January 2019

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542518080122

zbMATH Keywords

discontinuous Galerkin methodshallow water theoryhyperbolic system of conservation lawsintegral and local convergence order

Mathematics Subject Classification ID

Shock waves and blast waves in fluid mechanics (76L05) Hyperbolic conservation laws (35L65) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

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• Construction of high-order accurate shock-capturing finite difference schemes for unsteady shock waves
• Efficient implementation of weighted ENO schemes
• Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
• On the practical accuracy of shock-capturing schemes
• The Convergence Rate of Finite Difference Schemes in the Presence of Shocks
• Computational Considerations for the Simulation of Shock-Induced Sound
• The construction of difference schemes for hyperbolic equations based on characteristic relations
• Weak solutions of nonlinear hyperbolic equations and their numerical computation
• Monotonicity criteria for difference schemes designed for hyperbolic equations

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