Numerical solution of elliptic distributed optimal control problems with boundary value tracking
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914385775034368 |
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| author | Langer, Ulrich Löscher, Richard Steinbach, Olaf Yang, Huidong |
| author_facet | Langer, Ulrich Löscher, Richard Steinbach, Olaf Yang, Huidong |
| contents | We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be reformulated asa state-based variational problem that is the starting point for the finite element discretizion. In this paper, we only consider atensor-product finite element discretizion for which optimal discretization error estimates and fast solvers can be derived.Numerical experiments illustrate the theoretical results quantitatively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_27336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical solution of elliptic distributed optimal control problems with boundary value tracking Langer, Ulrich Löscher, Richard Steinbach, Olaf Yang, Huidong Numerical Analysis Optimization and Control We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be reformulated asa state-based variational problem that is the starting point for the finite element discretizion. In this paper, we only consider atensor-product finite element discretizion for which optimal discretization error estimates and fast solvers can be derived.Numerical experiments illustrate the theoretical results quantitatively. |
| title | Numerical solution of elliptic distributed optimal control problems with boundary value tracking |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2510.27336 |