Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916999511146496 |
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| author | Feng, Xiaobing Vo, Liet |
| author_facet | Feng, Xiaobing Vo, Liet |
| contents | This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative noise. Additionally, it introduces a novel approach and framework for the numerical analysis of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noise in general. The main ideas of this approach include establishing exponential stability estimates for the SPDE solution, leveraging a discrete stochastic Gronwall inequality, and employing a bootstrap argument. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization Feng, Xiaobing Vo, Liet Numerical Analysis This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative noise. Additionally, it introduces a novel approach and framework for the numerical analysis of nonlinear stochastic partial differential equations (SPDEs) with multiplicative noise in general. The main ideas of this approach include establishing exponential stability estimates for the SPDE solution, leveraging a discrete stochastic Gronwall inequality, and employing a bootstrap argument. |
| title | Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.08291 |