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Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions
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SYSNO ASEP 0531438 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions Author(s) Feireisl, Eduard (MU-W) RID, SAI, ORCID
Lukáčová-Medviďová, M. (DE)
Mizerová, Hana (MU-W) SAI, RIDSource Title Foundations of Computational Mathematics. - : Springer - ISSN 1615-3375
Roč. 20, č. 4 (2020), s. 923-966Number of pages 44 s. Language eng - English Country US - United States Keywords compressible Euler equations ; convergence ; dissipative measure-valued solution ; entropy stability ; entropy stable finite volume scheme Subject RIV BA - General Mathematics OECD category Pure mathematics Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000556090900008 EID SCOPUS 85070237869 DOI 10.1007/s10208-019-09433-z Annotation The Cauchy problem for the complete Euler system is in general ill-posed in the class of admissible (entropy producing) weak solutions. This suggests that there might be sequences of approximate solutions that develop fine-scale oscillations. Accordingly, the concept of measure-valued solution that captures possible oscillations is more suitable for analysis. We study the convergence of a class of entropy stable finite volume schemes for the barotropic and complete compressible Euler equations in the multidimensional case. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solution of the Euler system. Here dissipative means that a suitable form of the second law of thermodynamics is incorporated in the definition of the measure-valued solutions. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2021 Electronic address https://doi.org/10.1007/s10208-019-09433-z
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