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We propose and study a temporal, and spatio-temporal discretisation of the 2Dstochastic Navier--Stokes equations in bounded domains supplemented withno-slip boundary conditions. Considering additive noise, we base itsconstruction on the related nonlinear random PDE, which is solved by atransform of the solution of the stochastic Navier--Stokes equations. We showstrong rate (up to) $1$ in probability for a corresponding discretisation inspace and time (and space-time). Convergence of order (up to) 1 in time waspreviously only known for linear SPDEs.

Numerical analysis of 2D Navier--Stokes equations with additive stochastic forcing