Semigroup Splitting And Cubature Approximations For The Stochastic Navier-Stokes Equations

Abstract

Approximation of the marginal distribution of the solution of the stochastic Navier-Stokes equations on the two-dimensional torus by high order numerical methods is considered. The corresponding rates of convergence are obtained for a splitting scheme and the method of cubature on Wiener space applied to a spectral Galerkin discretisation of degree $N$. While the estimates exhibit a strong $N$ dependence, convergence is obtained for appropriately chosen time step sizes. Results of numerical simulations are provided, and confirm the applicability of the methods.

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• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations
• An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs