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

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Ľubomír Baňas, Dominic Breit, A. Chaudhary, Andreas Prohl
DOI: 10.48550/arxiv.2602.14268
Cited by: 0

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 $y = u- ΦW$, and different higher order numerical quadrature rules for the diffusion and the drift part. The theoretical findings are supported by numerical simulations.

Fields of Study & Subjects

Advanced Numerical Methods in Computational Mathematics Numerical methods for differential equations Navier-Stokes equation solutions

Publication details

Journal / source
arXiv (Cornell University)
Publication date
15 February 2026
Language
EN
Document type
Preprint