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Keldysh Institute preprints, 2018, 100, 22 pages (Mi ipmp2460)  

This article is cited in 5 scientific papers (total in 5 papers)

Entropic regularization of Discontinuous Galerkin method in one-dimensional problems of gas dynamics

Yu. A. Kriksin, V. F. Tishkin


Abstract: A new variational entropic regularization principle is formulated for a discontinuous Galerkin (DG) method. An entropy stable DG method of high accuracy is constructed for 1D equations of gas dynamics. The DG solutions satisfy the discrete analogues of the conservation laws of mass, momentum, total energy and entropic inequality. Formulas for the coefficients of the DG method are obtained.

Keywords: equations of gas dynamics, discontinuous Galerkin method, variational principle, conservation laws, entropy condition.

Funding Agency Grant Number
Russian Science Foundation 17-71-30014


DOI: https://doi.org/10.20948/prepr-2018-100

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Citation: Yu. A. Kriksin, V. F. Tishkin, “Entropic regularization of Discontinuous Galerkin method in one-dimensional problems of gas dynamics”, Keldysh Institute preprints, 2018, 100, 22 pp.

Citation in format AMSBIB
\Bibitem{KriTis18}
\by Yu.~A.~Kriksin, V.~F.~Tishkin
\paper Entropic regularization of Discontinuous Galerkin method in one-dimensional problems of gas dynamics
\jour Keldysh Institute preprints
\yr 2018
\papernumber 100
\totalpages 22
\mathnet{http://mi.mathnet.ru/ipmp2460}
\crossref{https://doi.org/10.20948/prepr-2018-100}
\elib{http://elibrary.ru/item.asp?id=34887801}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Verifikatsiya odnogo metoda entropiinoi regulyarizatsii razryvnykh skhem Galerkina dlya uravnenii giperbolicheskogo tipa”, Preprinty IPM im. M. V. Keldysha, 2019, 018, 25 pp.  mathnet  crossref  elib
    2. Yu. A. Kriksin, V. F. Tishkin, “Variatsionnaya entropiinaya regulyarizatsiya razryvnogo metoda Galerkina dlya uravnenii gazovoi dinamiki”, Matem. modelirovanie, 31:5 (2019), 69–84  mathnet  crossref  elib
    3. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Obespechenie entropiinoi ustoichivosti razryvnogo metoda Galerkina v gazodinamicheskikh zadachakh”, Preprinty IPM im. M. V. Keldysha, 2019, 051, 22 pp.  mathnet  crossref  elib
    4. Yu. A. Kriksin, V. F. Tishkin, “Chislennoe reshenie zadachi Einfeldta na osnove razryvnogo metoda Galerkina”, Preprinty IPM im. M. V. Keldysha, 2019, 090, 22 pp.  mathnet  crossref  elib
    5. M. D. Bragin, Yu. A. Kriksin, V. F. Tishkin, “Razryvnyi metod Galerkina s entropiinym ogranichitelem naklonov dlya uravnenii Eilera”, Matem. modelirovanie, 32:2 (2020), 113–128  mathnet  crossref
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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