On a PDE-based material parameter identification problem with contact constraints
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913104513728512 |
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| author | Hubmer, Simon Kindermann, Stefan Sherina, Ekaterina |
| author_facet | Hubmer, Simon Kindermann, Stefan Sherina, Ekaterina |
| contents | We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a PDE-based material parameter identification problem with contact constraints Hubmer, Simon Kindermann, Stefan Sherina, Ekaterina Numerical Analysis We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability. |
| title | On a PDE-based material parameter identification problem with contact constraints |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.08514 |