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arXiv · 2602.14268

A Higher Order Discretization for the Stochastic Navier--Stokes equations with additive Noise

L. Banas·D. Breit·A. Chaudhary·A. Prohl
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Abstract

We propose a new higher-order time discretization scheme for the stochastic Navier--Stokes equations with additive noise, where its velocity and pressure approximates converge at strong rate $1.5$ in probability. The construction rests on its reformulation as a random PDE for the transform $y = u- \Phi W$, and different higher order numerical quadrature rules for the diffusion and the drift part. The theoretical findings are supported by numerical simulations.

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L. Banas, D. Breit, A. Chaudhary, A. Prohl. 2026-02-15. A Higher Order Discretization for the Stochastic Navier--Stokes equations with additive Noise. https://arxiv.org/abs/2602.14268

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