We consider the 3D stochastic Navier-Stokes equation on the torus. Our main result concerns the temporal and spatio-temporal discretisation of a local strong pathwise solution. We prove optimal convergence rates in for the energy error with respect to convergence in probability, that is convergence of order 1 in space and of order (up to) 1/2 in time. The result holds up to the possible blow-up of the (time-discrete) solution. Our approach is based on discrete stopping times for the (time-discrete) solution.

翻译：我们考虑环面上的三维随机纳维-斯托克斯方程。主要结果涉及局部强轨道解的时间离散与时空离散化。我们证明了能量误差关于依概率收敛的最优收敛速率，即空间方向收敛阶为1，时间方向收敛阶（最高）为1/2。该结论在（时间离散）解可能发生爆破之前均成立。我们的方法基于（时间离散）解的离散停时。