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Mathematics > Numerical Analysis

arXiv:2304.00594 (math)
[Submitted on 2 Apr 2023]

Title:Convergence analysis of the Monte Carlo method for random Navier--Stokes--Fourier system

Authors:Maria Lukacova -- Medvidova, Bangwei She, Yuhuan Yuan
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Abstract:In the present paper we consider the initial data, external force, viscosity coefficients, and heat conductivity coefficient as random data for the compressible Navier--Stokes--Fourier system. The Monte Carlo method, which is frequently used for the approximation of statistical moments, is combined with a suitable deterministic discretisation method in physical space and time. Under the assumption that numerical densities and temperatures are bounded in probability, we prove the convergence of random finite volume solutions to a statistical strong solution by applying genuine stochastic compactness arguments. Further, we show the convergence and error estimates for the Monte Carlo estimators of the expectation and deviation. We present several numerical results to illustrate the theoretical results.
Comments: 24 pages, 5 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65C05, 76N06, 65M12, 80M60, 80M31
Cite as: arXiv:2304.00594 [math.NA]
  (or arXiv:2304.00594v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2304.00594

Submission history

From: Yuhuan Yuan [view email]
[v1] Sun, 2 Apr 2023 18:37:11 UTC (1,312 KB)
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