Error estimates of the Godunov method for the multidimensional compressible Euler system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557842" target="_blank" >RIV/67985840:_____/22:00557842 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10915-022-01843-6" target="_blank" >https://doi.org/10.1007/s10915-022-01843-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10915-022-01843-6" target="_blank" >10.1007/s10915-022-01843-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Error estimates of the Godunov method for the multidimensional compressible Euler system

Popis výsledku v původním jazyce

We derive a priori error estimates of the Godunov method for the multidimensional compressible Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance between the numerical solution and the strong solution. This yields also the estimates of the L2-norms of the errors in density, momentum and entropy. Under the assumption, that the numerical density is uniformly bounded from below by a positive constant and that the energy is uniformly bounded from above and stays positive, we obtain a convergence rate of 1/2 for the relative energy in the L1-norm, that is to say, a convergence rate of 1/4 for the L2-error of the numerical solution. Further, under the assumption—the total variation of the numerical solution is uniformly bounded, we obtain the first order convergence rate for the relative energy in the L1-norm, consequently, the numerical solution converges in the L2-norm with the convergence rate of 1/2. The numerical results presented are consistent with our theoretical analysis.

Název v anglickém jazyce

Error estimates of the Godunov method for the multidimensional compressible Euler system

Popis výsledku anglicky

We derive a priori error estimates of the Godunov method for the multidimensional compressible Euler system of gas dynamics. To this end we apply the relative energy principle and estimate the distance between the numerical solution and the strong solution. This yields also the estimates of the L2-norms of the errors in density, momentum and entropy. Under the assumption, that the numerical density is uniformly bounded from below by a positive constant and that the energy is uniformly bounded from above and stays positive, we obtain a convergence rate of 1/2 for the relative energy in the L1-norm, that is to say, a convergence rate of 1/4 for the L2-error of the numerical solution. Further, under the assumption—the total variation of the numerical solution is uniformly bounded, we obtain the first order convergence rate for the relative energy in the L1-norm, consequently, the numerical solution converges in the L2-norm with the convergence rate of 1/2. The numerical results presented are consistent with our theoretical analysis.

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

Journal of Scientific Computing

ISSN

0885-7474

e-ISSN

1573-7691

Svazek periodika

91

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

71

Kód UT WoS článku

000787294100001

EID výsledku v databázi Scopus

2-s2.0-85128890283