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

10/12/2021 ∙ by Dominic Breit, et al. ∙ 0

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.

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