Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system
Numerical Analysis
2021-11-16 v1 Numerical Analysis
Analysis of PDEs
Probability
Abstract
We propose a stochastic collocation method based on the piecewise constant interpolation on the probability space combined with a finite volume method to solve the compressible Navier-Stokes system at the nodal points. We show convergence of numerical solutions to a statistical solution of the Navier-Stokes system on condition that the numerical solutions are bounded in probability. The analysis uses the stochastic compactness method based on the Skorokhod/Jakubowski representation theorem and the criterion of convergence in probability due to Gy\"ongy and Krylov.
Keywords
Cite
@article{arxiv.2111.07435,
title = {Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system},
author = {Eduard Feireisl and Mária Lukáčová-Medvid'ová},
journal= {arXiv preprint arXiv:2111.07435},
year = {2021}
}