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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00574184" target="_blank" >RIV/67985840:_____/23:00574184 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1093/imanum/drac035" target="_blank" >https://doi.org/10.1093/imanum/drac035</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/imanum/drac035" target="_blank" >10.1093/imanum/drac035</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

We study a general convergence theory for the analysis of numerical solutions to a magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (=2,3). First, we introduce the concept of dissipative weak (DW) solutions and prove the weak-strong uniqueness property for DW solutions, meaning a DW solution coincides with a classical solution emanating from the same initial data on the lifespan of the latter. Next, we introduce the concept of consistent approximations and prove the convergence of consistent approximations towards the DW solution, as well as the classical solution. Interpreting the consistent approximation as the energy stability and consistency of numerical solutions, we have built a nonlinear variant of the celebrated Lax equivalence theorem. Finally, as an application of this theory, we show the convergence analysis of two numerical methods.

Název v anglickém jazyce

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

Popis výsledku anglicky

We study a general convergence theory for the analysis of numerical solutions to a magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (=2,3). First, we introduce the concept of dissipative weak (DW) solutions and prove the weak-strong uniqueness property for DW solutions, meaning a DW solution coincides with a classical solution emanating from the same initial data on the lifespan of the latter. Next, we introduce the concept of consistent approximations and prove the convergence of consistent approximations towards the DW solution, as well as the classical solution. Interpreting the consistent approximation as the energy stability and consistency of numerical solutions, we have built a nonlinear variant of the celebrated Lax equivalence theorem. Finally, as an application of this theory, we show the convergence analysis of two numerical methods.

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

2023

Kód důvěrnosti údajů

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

Název periodika

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

1464-3642

Svazek periodika

43

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

2169-2197

Kód UT WoS článku

000835418400001

EID výsledku v databázi Scopus

2-s2.0-85138478401