A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912427052892160 |
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| author | Nguyen, Quang Huy Hoang, Phuong Cuc Le, Van Chien Ta, Thi Thanh Mai |
| author_facet | Nguyen, Quang Huy Hoang, Phuong Cuc Le, Van Chien Ta, Thi Thanh Mai |
| contents | This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a discrete norm is established under a specific regularity assumption on the state and adjoint. Several numerical results are presented to corroborate our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10924 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization Nguyen, Quang Huy Hoang, Phuong Cuc Le, Van Chien Ta, Thi Thanh Mai Optimization and Control Numerical Analysis 35K20, 49N10, 65M15, 65M60 This paper investigates a space-time interface-fitted approximation of a moving-interface optimal control problem with energy regularization. We reformulate the optimality conditions into a variational problem involving both the state and adjoint. This problem is shown to be equivalent to our optimal control problem. Based on fully unstructured, space-time interface-fitted meshes, we propose and analyze a Petrov-Galerkin approximation of the problem. An optimal error estimate with respect to a discrete norm is established under a specific regularity assumption on the state and adjoint. Several numerical results are presented to corroborate our theoretical results. |
| title | A space-time interface-fitted method for moving-subdomain distributed control problems with energy regularization |
| topic | Optimization and Control Numerical Analysis 35K20, 49N10, 65M15, 65M60 |
| url | https://arxiv.org/abs/2506.10924 |