Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916605877813248 |
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| author | Ta, Thi Thanh Mai Nguyen, Quang Huy Hào, Dinh Nho |
| author_facet | Ta, Thi Thanh Mai Nguyen, Quang Huy Hào, Dinh Nho |
| contents | A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A space-time interface-fitted method is employed to discretize the advection-diffusion equation, where two second-order a priori error estimates are established with respect to the $L^2$-norms. Additionally, the regularized source is discretized sequentially using the variational approach, the element-wise constant discretization, and finally, the post-processing strategy. Optimal error estimates are achieved for the first two methods, while superlinear convergence is obtained for the third. Furthermore, a priori choices for the regularization parameter are proposed, depending on the mesh size and noise level. These choices ensure that the discrete and post-processing solutions strongly converge to the exact source as the mesh size and noise level tend to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains Ta, Thi Thanh Mai Nguyen, Quang Huy Hào, Dinh Nho Numerical Analysis 35R30, 65M15, 65M32, 65M60 A space-time interface-fitted approximation of an inverse source problem for the advection-diffusion equation with moving subdomains is investigated. The problem is reformulated as an optimization problem using Tikhonov regularization. A space-time interface-fitted method is employed to discretize the advection-diffusion equation, where two second-order a priori error estimates are established with respect to the $L^2$-norms. Additionally, the regularized source is discretized sequentially using the variational approach, the element-wise constant discretization, and finally, the post-processing strategy. Optimal error estimates are achieved for the first two methods, while superlinear convergence is obtained for the third. Furthermore, a priori choices for the regularization parameter are proposed, depending on the mesh size and noise level. These choices ensure that the discrete and post-processing solutions strongly converge to the exact source as the mesh size and noise level tend to zero. |
| title | Error analysis of the space-time interface-fitted finite element method for an inverse source problem for an advection-diffusion equation with moving subdomains |
| topic | Numerical Analysis 35R30, 65M15, 65M32, 65M60 |
| url | https://arxiv.org/abs/2502.06176 |