Study of a TPFA scheme for the stochastic Allen-Cahn problem with constraint through numerical experiments
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911410406031360 |
|---|---|
| author | Sapountzoglou, Niklas Zimmermann, Aleksandra |
| author_facet | Sapountzoglou, Niklas Zimmermann, Aleksandra |
| contents | This contribution provides numerical experiments for a finite volume scheme for an approximation of the stochastic Allen-Cahn equation with homogeneous Neumann boundary conditions. The approximation is done by a Yosida approximation of the subdifferential operator. The problem is set on a polygonal bounded domain in two or three dimensions. The non-linear character of the projection term induces challenges to implement the scheme. To this end, we provide a splitting method for the finite volume scheme. We show that the splitting method is accurate. The computational error estimates induce that the squared $L^2$-error w.r.t. time is of order $1$ as long as the noise term is small enough. For larger noise terms the order of convergence w.r.t. time might become worse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Study of a TPFA scheme for the stochastic Allen-Cahn problem with constraint through numerical experiments Sapountzoglou, Niklas Zimmermann, Aleksandra Numerical Analysis Analysis of PDEs Probability 60H15, 35K55, 65M08 This contribution provides numerical experiments for a finite volume scheme for an approximation of the stochastic Allen-Cahn equation with homogeneous Neumann boundary conditions. The approximation is done by a Yosida approximation of the subdifferential operator. The problem is set on a polygonal bounded domain in two or three dimensions. The non-linear character of the projection term induces challenges to implement the scheme. To this end, we provide a splitting method for the finite volume scheme. We show that the splitting method is accurate. The computational error estimates induce that the squared $L^2$-error w.r.t. time is of order $1$ as long as the noise term is small enough. For larger noise terms the order of convergence w.r.t. time might become worse. |
| title | Study of a TPFA scheme for the stochastic Allen-Cahn problem with constraint through numerical experiments |
| topic | Numerical Analysis Analysis of PDEs Probability 60H15, 35K55, 65M08 |
| url | https://arxiv.org/abs/2512.17712 |