AI 中文总结
研究具有加性噪声的三维随机纳维-斯托克斯方程，采用半隐式欧拉和克兰克-尼科尔森格式进行时间离散化，证明了不同格式的收敛速率，并通过数值模拟证实，首次对该方程进行了数值模拟。
AI 中文摘要
我们考虑具有加性随机强迫的三维随机纳维-斯托克斯方程。研究基于半隐式欧拉和克兰克-尼科尔森格式的时间离散化。证明了前一种格式在局部时间上收敛速率为1，后一种为3/2。这些理论结果通过大量数值模拟得到证实。据我们所知，这是首次对三维随机纳维-斯托克斯方程进行数值模拟。
英文摘要
We consider the three-dimensional stochastic Navier--Stokes equations with additive stochastic forcing. We study temporal discretizations based on a semi-implicit Euler as well as a Crank-Nicolson scheme. We prove that locally in time the former converges with rate 1 while the latter converges with rate 3/2. These theoretical results are confirmed by extensive numerical simulations. To the best of our knowledge this is the first time that numerical simulations for the three-dimensional stochastic Navier--Stokes equations have been performed.
