Standard

On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves. / Ladonkina, M. E.; Neklyudova, O. A.; Ostapenko, V. V. et al.

In: Computational Mathematics and Mathematical Physics, Vol. 58, No. 8, 01.08.2018, p. 1344-1353.

Research output: Contribution to journal › Article › peer-review

Harvard

Ladonkina, ME, Neklyudova, OA, Ostapenko, VV & Tishkin, VF 2018, 'On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves', Computational Mathematics and Mathematical Physics, vol. 58, no. 8, pp. 1344-1353. https://doi.org/10.1134/S0965542518080122

APA

Ladonkina, M. E., Neklyudova, O. A., Ostapenko, V. V., & Tishkin, V. F. (2018). On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves. Computational Mathematics and Mathematical Physics, 58(8), 1344-1353. https://doi.org/10.1134/S0965542518080122

Vancouver

Ladonkina ME, Neklyudova OA, Ostapenko VV, Tishkin VF. On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves. Computational Mathematics and Mathematical Physics. 2018 Aug 1;58(8):1344-1353. doi: 10.1134/S0965542518080122

Author

Ladonkina, M. E. ; Neklyudova, O. A. ; Ostapenko, V. V. et al. / On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves. In: Computational Mathematics and Mathematical Physics. 2018 ; Vol. 58, No. 8. pp. 1344-1353.

BibTeX

@article{cbc5590b30d547e8b55770c4df61a456,
title = "On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves",
abstract = "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.",
keywords = "discontinuous Galerkin method, hyperbolic system of conservation laws, integral and local convergence order, shallow water theory, CONVERGENCE, DIFFERENCE-SCHEMES, HYPERBOLIC CONSERVATION-LAWS",
author = "Ladonkina, {M. E.} and Neklyudova, {O. A.} and Ostapenko, {V. V.} and Tishkin, {V. F.}",
note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",
year = "2018",
month = aug,
day = "1",
doi = "10.1134/S0965542518080122",
language = "English",
volume = "58",
pages = "1344--1353",
journal = "Computational Mathematics and Mathematical Physics",
issn = "0965-5425",
publisher = "PLEIADES PUBLISHING INC",
number = "8",

}

RIS

TY - JOUR

T1 - On the Accuracy of the Discontinuous Galerkin Method in Calculation of Shock Waves

AU - Ladonkina, M. E.

AU - Neklyudova, O. A.

AU - Ostapenko, V. V.

AU - Tishkin, V. F.

N1 - Publisher Copyright: © 2018, Pleiades Publishing, Ltd.

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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.

AB - 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.

KW - discontinuous Galerkin method

KW - hyperbolic system of conservation laws

KW - integral and local convergence order

KW - shallow water theory

KW - CONVERGENCE

KW - DIFFERENCE-SCHEMES

KW - HYPERBOLIC CONSERVATION-LAWS

UR - http://www.scopus.com/inward/record.url?scp=85053924455&partnerID=8YFLogxK

U2 - 10.1134/S0965542518080122

DO - 10.1134/S0965542518080122

M3 - Article

AN - SCOPUS:85053924455

VL - 58

SP - 1344

EP - 1353

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 8

ER -

ID: 16757911