Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA21-02411S" target="_blank" >GA21-02411S: Solving ill posed problems in the dynamics of compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Models and Methods in Applied Sciences
ISSN
0218-2025
e-ISSN
1793-6314
Volume of the periodical
32
Issue of the periodical within the volume
14
Country of publishing house
SG - SINGAPORE
Number of pages
39
Pages from-to
2887-2925
UT code for WoS article
000900774200002
EID of the result in the Scopus database
2-s2.0-85144563178