We propose and study a temporal, and spatio-temporal discretisation of the 2D stochastic Navier--Stokes equations in bounded domains supplemented with no-slip boundary conditions. Considering additive noise, we base its construction on the related nonlinear random PDE, which is solved by a transform of the solution of the stochastic Navier--Stokes equations. We show strong rate (up to) $1$ in probability for a corresponding discretisation in space and time (and space-time). Convergence of order (up to) 1 in time was previously only known for linear SPDEs.

翻译：我们提出并研究在以无滑坡边界条件补充的封闭域内2D 随机导航-斯托克方程式的暂时和时空分解。考虑到添加性噪音,我们将其建筑建立在相关的非线性随机PDE的基础上,通过转换随机导航-斯托克方程式的解决方案来解决。我们显示出在时空间(和时空)相应分解的强烈率(高达1美元 ) 。 此前只有线性SPDE才知道秩序的趋同(最多1美元 ) 。