CONVERGENCE OF A STOCHASTIC COLLOCATION FINITE VOLUME METHOD FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM

• 成果类型: Article
• 署名作者: Feireisl, Eduard; Cova-medvidova, Maria Luka
• 署名单位: Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; Johannes Gutenberg University of Mainz
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1937
• 发表日期: 2023
• 页码: 4936-4963
• 关键词: partial-differential-equations; Error analysis; elliptic pdes; approximations; scheme

摘要

We propose a stochastic collocation method based on the piecewise con -stant 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 con-vergence in probability due to Gyongy and Krylov.