Convergence of a finite volume scheme for the compressible Navier–Stokes system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1957-1979.

We study convergence of a finite volume scheme for the compressible (barotropic) Navier–Stokes system. First we prove the energy stability and consistency of the scheme and show that the numerical solutions generate a dissipative measure-valued solution of the system. Then by the dissipative measure-valued-strong uniqueness principle, we conclude the convergence of the numerical solution to the strong solution as long as the latter exists. Numerical experiments for standard benchmark tests support our theoretical results.

DOI : 10.1051/m2an/2019043
Classification : 35Q30, 65N12, 76M12, 76NXX
Mots-clés : Compressible Navier–Stokes system, convergence, dissipative measure valued solution, finite volume method
Feireisl, Eduard 1 ; Lukáčová-Medvid’ová, Mária 1 ; Mizerová, Hana 1 ; She, Bangwei 1

1 
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     author = {Feireisl, Eduard and Luk\'a\v{c}ov\'a-Medvid{\textquoteright}ov\'a, M\'aria and Mizerov\'a, Hana and She, Bangwei},
     title = {Convergence of a finite volume scheme for the compressible {Navier{\textendash}Stokes} system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1957--1979},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {6},
     year = {2019},
     doi = {10.1051/m2an/2019043},
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     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2019043/}
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Feireisl, Eduard; Lukáčová-Medvid’ová, Mária; Mizerová, Hana; She, Bangwei. Convergence of a finite volume scheme for the compressible Navier–Stokes system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 53 (2019) no. 6, pp. 1957-1979. doi : 10.1051/m2an/2019043. http://www.numdam.org/articles/10.1051/m2an/2019043/

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