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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 8, Pages 148–156 (Mi zvmmf10770)  

This article is cited in 1 scientific paper (total in 1 paper)

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

M. E. Ladonkinaa, O. A. Neklyudovab, V. V. Ostapenkoc, V. F. Tishkinc

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
b Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
c Novosibirsk State University, Novosibirsk, Russia

Abstract: The accuracy of the discontinuous Galerkin method of the third-order approximation on smooth solutions in the calculation of discontinuous solutions of a quasilinear hyperbolic system of conservation laws with shock waves propagating with a variable velocity is studied. As an example, the approximation of the system of conservation laws of shallow water theory is considered. On the example of this system, it is shown that, like the TVD and WENO schemes of increased order of approximation on smooth solutions, the discontinuous Galerkin method, despite its high accuracy on smooth solutions and in the localization of shock waves, reduces its order of convergence to the first order in the shock wave influence domain.

Key words: hyperbolic system of conservation laws, discontinuous Galerkin method, shallow water theory, integral and local convergence order.

Funding Agency Grant Number
Russian Science Foundation 16-11-10033


DOI: https://doi.org/10.31857/S004446690002009-0

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:8, 1344–1353

Bibliographic databases:

UDC: 519.633
Received: 05.03.2018

Citation: M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “On the accuracy of the discontinuous Galerkin method in calculation of shock waves”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 148–156; Comput. Math. Math. Phys., 58:8 (2018), 1344–1353

Citation in format AMSBIB
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\vol 58
\issue 8
\pages 148--156
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\pages 1344--1353
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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