Computational unique continuation with finite dimensional Neumann trace
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913731546447872 |
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| author | Burman, Erik Oksanen, Lauri Zhao, Ziyao |
| author_facet | Burman, Erik Oksanen, Lauri Zhao, Ziyao |
| contents | We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative error estimates we prove Lipschitz stability of the unique continuation problem in the global H1-norm. This stability is then leveraged to derive optimal a posteriori and a priori error estimates for a primal-dual stabilised finite method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computational unique continuation with finite dimensional Neumann trace Burman, Erik Oksanen, Lauri Zhao, Ziyao Numerical Analysis 65N20 We consider finite element approximations of unique continuation problems subject to elliptic equations in the case where the normal derivative of the exact solution is known to reside in some finite dimensional space. To give quantitative error estimates we prove Lipschitz stability of the unique continuation problem in the global H1-norm. This stability is then leveraged to derive optimal a posteriori and a priori error estimates for a primal-dual stabilised finite method. |
| title | Computational unique continuation with finite dimensional Neumann trace |
| topic | Numerical Analysis 65N20 |
| url | https://arxiv.org/abs/2402.13695 |