On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00562018" target="_blank" >RIV/67985840:_____/22:00562018 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/21M1431011" target="_blank" >https://doi.org/10.1137/21M1431011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/21M1431011" target="_blank" >10.1137/21M1431011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field

Popis výsledku v původním jazyce

We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence-free property of magnetic field exactly. Our strategy utilizes the recent concepts of dissipative weak solutions and consistent approximations. First, we show the dissipative weak-strong uniqueness principle, meaning a dissipative weak solution coincides with a classical solution as long as they emanate from the same initial data. Next, we show the convergence of consistent approximation toward the dissipative weak solution and thus the classical solution. Upon interpreting the consistent approximation as the stability and consistency of suitable numerical solutions we have established a generalized Lax equivalence theory: convergence - stability and consistency. Further, to illustrate the application of this theory, we propose two mixed finite volume-finite element methods with exact divergence-free magnetic field. Finally, by showing that solutions of these two schemes are consistent approximations, we conclude their convergence toward the dissipative weak solution and the classical solution.

Název v anglickém jazyce

On convergence of numerical solutions for the compressible MHD system with exactly divergence-free magnetic field

Popis výsledku anglicky

We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence-free property of magnetic field exactly. Our strategy utilizes the recent concepts of dissipative weak solutions and consistent approximations. First, we show the dissipative weak-strong uniqueness principle, meaning a dissipative weak solution coincides with a classical solution as long as they emanate from the same initial data. Next, we show the convergence of consistent approximation toward the dissipative weak solution and thus the classical solution. Upon interpreting the consistent approximation as the stability and consistency of suitable numerical solutions we have established a generalized Lax equivalence theory: convergence - stability and consistency. Further, to illustrate the application of this theory, we propose two mixed finite volume-finite element methods with exact divergence-free magnetic field. Finally, by showing that solutions of these two schemes are consistent approximations, we conclude their convergence toward the dissipative weak solution and the classical solution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-02411S" target="_blank" >GA21-02411S: Řešení nekorektních úloh pohybu stlačitelných tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Numerical Analysis

ISSN

0036-1429

e-ISSN

1095-7170

Svazek periodika

60

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

2182-2202

Kód UT WoS článku

000862256800008

EID výsledku v databázi Scopus

2-s2.0-85138475265