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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.17315 |
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| _version_ | 1866910145928232960 |
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| author | Chowdhury, Sudipto Shallu |
| author_facet | Chowdhury, Sudipto Shallu |
| contents | This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two-dimensional bounded, convex, polygonal domain. It employs an ultra-weak formulation and utilizes Crouzeix-Raviart finite elements to discretize the state variable, while employing piecewise constants for the control variable discretization. Furthermore, it establishes an optimal order a priori error estimate for the control variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17315 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Crouzeix-Raviart Finite Element Approximation of Dirichlet Boundary Control Problems with Piecewise Constant Controls Chowdhury, Sudipto Shallu Optimization and Control This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two-dimensional bounded, convex, polygonal domain. It employs an ultra-weak formulation and utilizes Crouzeix-Raviart finite elements to discretize the state variable, while employing piecewise constants for the control variable discretization. Furthermore, it establishes an optimal order a priori error estimate for the control variable. |
| title | Crouzeix-Raviart Finite Element Approximation of Dirichlet Boundary Control Problems with Piecewise Constant Controls |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.17315 |