A surface finite element scheme for a stochastic PDE on an evolving curve
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918079490949120 |
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| author | Pozzi, Paola Stinner, Björn |
| author_facet | Pozzi, Paola Stinner, Björn |
| contents | In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise) which in particular destroys the classical time differentiability properties of the solution. We provide a suitable variational solution concept and a fully discrete FEM discretization. Our error analysis appropriately generalizes classical estimates to this weaker setting. We present some numerical simulations that confirm our theoretical findings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_01527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A surface finite element scheme for a stochastic PDE on an evolving curve Pozzi, Paola Stinner, Björn Numerical Analysis 60H35, 65M60, 65M15 In this paper we consider an ESFEM method for the advection and diffusion of a scalar quantity on a moving closed curve. The diffusion process is controlled by a forcing term that may include a rough term (specifically a stochastic noise) which in particular destroys the classical time differentiability properties of the solution. We provide a suitable variational solution concept and a fully discrete FEM discretization. Our error analysis appropriately generalizes classical estimates to this weaker setting. We present some numerical simulations that confirm our theoretical findings. |
| title | A surface finite element scheme for a stochastic PDE on an evolving curve |
| topic | Numerical Analysis 60H35, 65M60, 65M15 |
| url | https://arxiv.org/abs/2507.01527 |