Finite volumes for the Gross-Pitaevskii equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914030879244288 |
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| author | Chauleur, Quentin |
| author_facet | Chauleur, Quentin |
| contents | We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We finally perform some numerical simulations to investigate convergence error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03821 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite volumes for the Gross-Pitaevskii equation Chauleur, Quentin Numerical Analysis We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We finally perform some numerical simulations to investigate convergence error. |
| title | Finite volumes for the Gross-Pitaevskii equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.03821 |