Error Estimate for a Semi-Lagrangian Scheme for Hamilton-Jacobi Equations on Networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915571829833728 |
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| author | Carlini, Elisabetta Coscetti, Valentina Pozza, Marco |
| author_facet | Carlini, Elisabetta Coscetti, Valentina Pozza, Marco |
| contents | We examine the numerical approximation of time-dependent Hamilton-Jacobi equations on networks, providing a convergence error estimate for the semi-Lagrangian scheme introduced in (Carlini and Siconolfi, 2023), where convergence was proven without an error estimate. We derive a convergence error estimate of order one-half. This is achieved showing the equivalence between two definitions of solutions to this problem proposed in (Imbert and Monneau, 2017) and (Siconolfi, 2022), a result of independent interest, and applying a general convergence result from (Carlini, Festa and Forcadel, 2020). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Estimate for a Semi-Lagrangian Scheme for Hamilton-Jacobi Equations on Networks Carlini, Elisabetta Coscetti, Valentina Pozza, Marco Numerical Analysis Analysis of PDEs 65M15, 49L25, 65M12, 35R02 We examine the numerical approximation of time-dependent Hamilton-Jacobi equations on networks, providing a convergence error estimate for the semi-Lagrangian scheme introduced in (Carlini and Siconolfi, 2023), where convergence was proven without an error estimate. We derive a convergence error estimate of order one-half. This is achieved showing the equivalence between two definitions of solutions to this problem proposed in (Imbert and Monneau, 2017) and (Siconolfi, 2022), a result of independent interest, and applying a general convergence result from (Carlini, Festa and Forcadel, 2020). |
| title | Error Estimate for a Semi-Lagrangian Scheme for Hamilton-Jacobi Equations on Networks |
| topic | Numerical Analysis Analysis of PDEs 65M15, 49L25, 65M12, 35R02 |
| url | https://arxiv.org/abs/2411.02356 |