Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00531438" target="_blank" >RIV/67985840:_____/20:00531438 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10208-019-09433-z" target="_blank" >https://doi.org/10.1007/s10208-019-09433-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10208-019-09433-z" target="_blank" >10.1007/s10208-019-09433-z</a>
Alternative languages
Result language
angličtina
Original language name
Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Foundations of Computational Mathematics
ISSN
1615-3375
e-ISSN
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Volume of the periodical
20
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
44
Pages from-to
923-966
UT code for WoS article
000556090900008
EID of the result in the Scopus database
2-s2.0-85070237869