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arXiv · 2111.07435

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

Eduard Feireisl·Mária Lukáčová-Medvid'ová
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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.

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Eduard Feireisl, Mária Lukáčová-Medvid'ová. 2021-11-14. Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system. https://arxiv.org/abs/2111.07435

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