Report
A fitted space-time finite element method for an advection-diffusion problem with moving interfaces
| العنوان: | A fitted space-time finite element method for an advection-diffusion problem with moving interfaces |
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| المؤلفون: | Nguyen, Quang Huy, Le, Van Chien, Hoang, Phuong Cuc, Ta, Thi Thanh Mai |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | 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. Comment: 20 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.apnum.2025.01.002 |
| URL الوصول: | http://arxiv.org/abs/2407.08439 |
| رقم الانضمام: | edsarx.2407.08439 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.apnum.2025.01.002 |
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