Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00569928" target="_blank" >RIV/67985840:_____/22:00569928 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0218202522500671" target="_blank" >https://doi.org/10.1142/S0218202522500671</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202522500671" target="_blank" >10.1142/S0218202522500671</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method

Popis výsledku v původním jazyce

The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic discretization scheme, such as a finite volume (FV) method. We assume that the initial data, force and the viscosity coefficients are random variables and study both the statistical convergence rates as well as the approximation errors. Since the compressible Navier-Stokes equations are not known to be uniquely solvable in the class of global weak solutions, we cannot apply pathwise arguments to analyze the random Navier-Stokes equations. Instead, we have to apply intrinsic stochastic compactness arguments via the Skorokhod representation theorem and the Gyöngy-Krylov method. Assuming that the numerical solutions are bounded in probability, we prove that the Monte Carlo FV method converges to a statistical strong solution. The convergence rates are discussed as well. Numerical experiments illustrate theoretical results.

Název v anglickém jazyce

Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method

Popis výsledku anglicky

The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic discretization scheme, such as a finite volume (FV) method. We assume that the initial data, force and the viscosity coefficients are random variables and study both the statistical convergence rates as well as the approximation errors. Since the compressible Navier-Stokes equations are not known to be uniquely solvable in the class of global weak solutions, we cannot apply pathwise arguments to analyze the random Navier-Stokes equations. Instead, we have to apply intrinsic stochastic compactness arguments via the Skorokhod representation theorem and the Gyöngy-Krylov method. Assuming that the numerical solutions are bounded in probability, we prove that the Monte Carlo FV method converges to a statistical strong solution. The convergence rates are discussed as well. Numerical experiments illustrate theoretical results.

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

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

1793-6314

Svazek periodika

32

Číslo periodika v rámci svazku

14

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

39

Strana od-do

2887-2925

Kód UT WoS článku

000900774200002

EID výsledku v databázi Scopus

2-s2.0-85144563178