Distributed optimal control problems governed by poroelasticity equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911731146555392 |
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| author | Khan, Arbaz Lee, Jeonghun J. Singh, Harpal |
| author_facet | Khan, Arbaz Lee, Jeonghun J. Singh, Harpal |
| contents | In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poroelasticity. Firstly, we prove the well-posedness of the new formulation and then show the existence and uniqueness of optimal control where the fluid sources in the model act as a control variable. We prove a priori error estimates for the fully discrete scheme with backward Euler time discretization and a variational approximation of the control variable. A numerical example is presented to validate the performance of the proposed novel scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributed optimal control problems governed by poroelasticity equations Khan, Arbaz Lee, Jeonghun J. Singh, Harpal Optimization and Control Numerical Analysis 65M12, 65M15, 65M60, 76S99 In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poroelasticity. Firstly, we prove the well-posedness of the new formulation and then show the existence and uniqueness of optimal control where the fluid sources in the model act as a control variable. We prove a priori error estimates for the fully discrete scheme with backward Euler time discretization and a variational approximation of the control variable. A numerical example is presented to validate the performance of the proposed novel scheme. |
| title | Distributed optimal control problems governed by poroelasticity equations |
| topic | Optimization and Control Numerical Analysis 65M12, 65M15, 65M60, 76S99 |
| url | https://arxiv.org/abs/2605.30839 |