On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves
- Authors: Ladonkina M.E.1, Neklyudova O.A.2, Ostapenko V.V.3, Tishkin V.F.3
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Affiliations:
- Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
- Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 58, No 8 (2018)
- Pages: 1344-1353
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179802
- DOI: https://doi.org/10.1134/S0965542518080122
- ID: 179802
Cite item
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.
About the authors
M. E. Ladonkina
Keldysh Institute of Applied Mathematics, Russian Academy of Sciences
Author for correspondence.
Email: ladonkina@imamod.ru
Russian Federation, Moscow, 125047
O. A. Neklyudova
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences
Email: ladonkina@imamod.ru
Russian Federation, Novosibirsk, 630090
V. V. Ostapenko
Novosibirsk State University
Email: ladonkina@imamod.ru
Russian Federation, Novosibirsk, 630090
V. F. Tishkin
Novosibirsk State University
Email: ladonkina@imamod.ru
Russian Federation, Novosibirsk, 630090
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