Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system

2021/11/14 by Eduard Feireisl, Feireisl, Eduard, Mária Lukáčová-Medviďová +1
Decision Sciences · Economics, Econometrics and Finance · #35Q35 #35Q49 #60H35 #65C20 #65N08 #76N06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.07435

openalex publication_date 2021/11/14 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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 Gyöngy and Krylov.

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