Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915454983864320 |
|---|---|
| author | Hu, Tianhao Huang, Xinchi Jin, Bangti Quan, Qimeng Zhou, Zhi |
| author_facet | Hu, Tianhao Huang, Xinchi Jin, Bangti Quan, Qimeng Zhou, Zhi |
| contents | In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and Hölder stability for the inverse problem with and without boundary conditions, respectively, using suitable Carleman estimates. Then we propose a numerical approach for solving the inverse problem using conforming finite element approximations in both time and space. Moreover, by utilizing the conditional stability estimates, we prove rigorous error bounds on the discrete approximation. We present several numerical experiments to illustrate the effectiveness of the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates Hu, Tianhao Huang, Xinchi Jin, Bangti Quan, Qimeng Zhou, Zhi Numerical Analysis In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and Hölder stability for the inverse problem with and without boundary conditions, respectively, using suitable Carleman estimates. Then we propose a numerical approach for solving the inverse problem using conforming finite element approximations in both time and space. Moreover, by utilizing the conditional stability estimates, we prove rigorous error bounds on the discrete approximation. We present several numerical experiments to illustrate the effectiveness of the approach. |
| title | Conditional Stability and Numerical Reconstruction of a Parabolic Inverse Source Problem Using Carleman Estimates |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.15406 |