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Matematicheskoe modelirovanie, 2021, Volume 33, Number 3, Pages 98–108
DOI: https://doi.org/10.20948/mm-2021-03-07 (Mi mm4274) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On increasing the stability of the combined scheme of the discontinuous Galerkin method

M. E. Ladonkinaab, O. A. Nekliudovaab, V. V. Ostapenkob, V. F. Tishkinba

a Keldysh Institute of Applied Mathematics of RAS, Moscow
b Lavrentiev Institute of Hydrodynamics, Novosibirsk
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DOI: https://doi.org/10.20948/mm-2021-03-07
Abstract: A special modification of the combined scheme of the discontinuous Galerkin method is proposed, which increases the stability of this scheme when calculating discontinuous solutions with shock waves. This modification is associated with the addition of an artificial viscosity of the fourth order of divergence to the basic scheme included in this combined scheme. Test calculations are presented. They demonstrate the advantages of the new combined scheme in comparison with the standard monotonized versions of the discontinuous Galerkin method.
Keywords: systems of conservation laws, combined schemes, discontinuous Galerkin method, artificial viscosity.
Funding agency Grant number
Russian Science Foundation 16-11-10033
Received: 26.10.2020
Revised: 26.10.2020
Accepted: 30.11.2020
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 6, Pages 979–985
DOI: https://doi.org/10.1134/S2070048221060119
Document Type: Article
Language: Russian
Citation: M. E. Ladonkina, O. A. Nekliudova, V. V. Ostapenko, V. F. Tishkin, “On increasing the stability of the combined scheme of the discontinuous Galerkin method”, Matem. Mod., 33:3 (2021), 98–108; Math. Models Comput. Simul., 13:6 (2021), 979–985
Citation in format AMSBIB
\Bibitem{LadNekOst21}
\by M.~E.~Ladonkina, O.~A.~Nekliudova, V.~V.~Ostapenko, V.~F.~Tishkin
\paper On increasing the stability of the combined scheme of the discontinuous Galerkin method
\jour Matem. Mod.
\yr 2021
\vol 33
\issue 3
\pages 98--108
\mathnet{http://mi.mathnet.ru/mm4274}
\crossref{https://doi.org/10.20948/mm-2021-03-07}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 6
\pages 979--985
\crossref{https://doi.org/10.1134/S2070048221060119}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математическое моделирование
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