Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910714999865344 |
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| author | Li, Binjie Zhou, Qin |
| author_facet | Li, Binjie Zhou, Qin |
| contents | This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial approximation. A pathwise uniform convergence rate is derived, encompassing general spatial \( L^q \)-norms, by using discrete versions of deterministic and stochastic maximal \( L^p \)-regularity estimates. Additionally, the theoretical convergence rate is validated through numerical experiments. The primary contribution of this work is the introduction of a technique to establish the pathwise uniform convergence of finite element-based full discretizations for nonlinear stochastic parabolic equations within the framework of general spatial \( L^q \)-norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise Li, Binjie Zhou, Qin Numerical Analysis 60H35, 35R60, 60H15 This paper analyzes a full discretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. The discretization combines the Euler scheme for temporal approximation and the finite element method for spatial approximation. A pathwise uniform convergence rate is derived, encompassing general spatial \( L^q \)-norms, by using discrete versions of deterministic and stochastic maximal \( L^p \)-regularity estimates. Additionally, the theoretical convergence rate is validated through numerical experiments. The primary contribution of this work is the introduction of a technique to establish the pathwise uniform convergence of finite element-based full discretizations for nonlinear stochastic parabolic equations within the framework of general spatial \( L^q \)-norms. |
| title | Pathwise uniform convergence of a full discretization for a three-dimensional stochastic Allen-Cahn equation with multiplicative noise |
| topic | Numerical Analysis 60H35, 35R60, 60H15 |
| url | https://arxiv.org/abs/2405.03016 |