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. Assuming Lipschitz-continuous diffusion coefficients and under mild conditions on the initial data, we establish that the full discretization achieves linear 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。在扩散系数满足Lipschitz连续且初始数据满足温和条件的假设下，我们证明了全离散格式在空间上具有线性收敛阶，在时间上具有近半阶收敛阶。