Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Foundations of Computational Mathematics

ISSN

1615-3375

e-ISSN

—

Svazek periodika

20

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

923-966

Kód UT WoS článku

000556090900008

EID výsledku v databázi Scopus

2-s2.0-85070237869