A fitted space-time finite element method for an advection-diffusion problem with moving interfaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929669242093568 |
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| author | Nguyen, Quang Huy Le, Van Chien Hoang, Phuong Cuc Ta, Thi Thanh Mai |
| author_facet | Nguyen, Quang Huy Le, Van Chien Hoang, Phuong Cuc Ta, Thi Thanh Mai |
| contents | This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08439 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fitted space-time finite element method for an advection-diffusion problem with moving interfaces Nguyen, Quang Huy Le, Van Chien Hoang, Phuong Cuc Ta, Thi Thanh Mai Numerical Analysis This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution gradient across the interface. We use the Banach-Necas-Babuska theorem to show the well-posedness of the continuous variational problem. A fully discrete finite-element based scheme is analyzed using the Galerkin method and unstructured interface-fitted meshes. An optimal error estimate is established in a discrete energy norm under a globally low but locally high regularity condition. Some numerical results corroborate our theoretical results. |
| title | A fitted space-time finite element method for an advection-diffusion problem with moving interfaces |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2407.08439 |