Numerical approximation of the stochastic Cahn-Hilliard equation with space-time white noise near the sharp interface limit
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916556466814976 |
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| author | Baňas, Ľubomír Mukam, Jean Daniel |
| author_facet | Baňas, Ľubomír Mukam, Jean Daniel |
| contents | We consider the stochastic Cahn-Hilliard equation with additive space-time white noise $ε^γ\dot{W}$ in dimension $d=2,3$, where $ε>0$ is an interfacial width parameter. We study numerical approximation of the equation which combines a structure preserving implicit time-discretization scheme with a discrete approximation of the space-time white noise. We derive a strong error estimate for the considered numerical approximation which is robust with respect to the inverse of the interfacial width parameter $ε$. Furthermore, by a splitting approach, we show that for sufficiently large scaling parameter $γ$, the numerical approximation of the stochastic Cahn-Hilliard equation converges uniformly to the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp interface limit $ε\rightarrow 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12832 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical approximation of the stochastic Cahn-Hilliard equation with space-time white noise near the sharp interface limit Baňas, Ľubomír Mukam, Jean Daniel Numerical Analysis We consider the stochastic Cahn-Hilliard equation with additive space-time white noise $ε^γ\dot{W}$ in dimension $d=2,3$, where $ε>0$ is an interfacial width parameter. We study numerical approximation of the equation which combines a structure preserving implicit time-discretization scheme with a discrete approximation of the space-time white noise. We derive a strong error estimate for the considered numerical approximation which is robust with respect to the inverse of the interfacial width parameter $ε$. Furthermore, by a splitting approach, we show that for sufficiently large scaling parameter $γ$, the numerical approximation of the stochastic Cahn-Hilliard equation converges uniformly to the deterministic Hele-Shaw/Mullins-Sekerka problem in the sharp interface limit $ε\rightarrow 0$. |
| title | Numerical approximation of the stochastic Cahn-Hilliard equation with space-time white noise near the sharp interface limit |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2401.12832 |