A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915110664011776 |
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| author | Castro, Carlos Micu, Sorin |
| author_facet | Castro, Carlos Micu, Sorin |
| contents | We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem using a space discretization based on a mixed finite element method is proposed and analyzed. Its stability and convergence relay on a new uniform boundary observability property with respect to the discretization parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability Castro, Carlos Micu, Sorin Numerical Analysis Optimization and Control 35R30, 93B07, 65M60 We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem using a space discretization based on a mixed finite element method is proposed and analyzed. Its stability and convergence relay on a new uniform boundary observability property with respect to the discretization parameter. |
| title | A mixed finite elements approximation of inverse source problems for the wave equation with variable coefficients using observability |
| topic | Numerical Analysis Optimization and Control 35R30, 93B07, 65M60 |
| url | https://arxiv.org/abs/2501.11352 |