This paper investigates the pathwise uniform convergence in probability of fully discrete finite-element approximations for the two-dimensional stochastic Navier-Stokes equations with multiplicative noise, subject to no-slip boundary conditions. We demonstrate that the full discretization achieves nearly $ 3/2$-order convergence in space and nearly half-order convergence in time.

翻译：本文研究了具有乘性噪声的二维随机Navier-Stokes方程在无滑移边界条件下全离散有限元逼近的路径一致概率收敛性。我们证明了该全离散格式在空间上达到近$3/2$阶收敛，在时间上达到近半阶收敛。