随机正压可压缩欧拉方程的收敛有限体积格式。

Pub Date : 2023-10-23 DOI:10.1051/m2an/2023085
Abhishek Chaudhary, Ujjwal Koley
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引用次数: 1

摘要

本文分析了由乘性布朗噪声驱动的三维正压可压缩欧拉方程的半离散有限体积格式。我们导出了数值近似的必要先验估计,并证明了由数值近似产生的Young测度收敛于随机可压缩欧拉系统的耗散测度值鞅解。这些解决方案在概率上是弱的,因为驱动噪声和相关过滤是解决方案的组成部分。此外,由于底层系统的弱(测量值)-强唯一性原理,我们证明了极限系统的正则解的数值解至少在后者的寿命上是强收敛的。据我们所知,这是第一次尝试证明底层系统的数值近似的收敛性。
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A convergent finite volume scheme for the stochastic barotropic compressible Euler equations.
In this paper, we analyze a semi-discrete finite volume scheme for the three dimensional barotropic compressible Euler equations driven by a multiplicative Brownian noise. We derive necessary a priori estimates for numerical approximations, and show that the Young measure generated by the numerical approximations converge to a dissipative measure--valued martingale solution to the stochastic compressible Euler system. These solutions are probabilistically weak in the sense that the driving noise and associated filtration are integral part of the solution. Moreover, we demonstrate strong convergence of numerical solutions to the regular solution of the limit systems at least on the lifespan of the latter, thanks to the weak (measure-valued)--strong uniqueness principle for the underlying system. To the best of our knowledge, this is the first attempt to prove the convergence of numerical approximations for the underlying system.
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