Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin System
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914825258401792 |
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| author | Bessemoulin-Chatard, Marianne Mathis, Hélène |
| author_facet | Bessemoulin-Chatard, Marianne Mathis, Hélène |
| contents | This paper deals with the diffusive limit of the Jin and Xin model and its approximation by an asymptotic preserving finite volume scheme. At the continuous level, we determine a convergence rate to the diffusive limit by means of a relative entropy method. Considering a semi-discrete approximation (discrete in space and continuous in time), we adapt the method to this semi-discrete framework and establish that the approximated solutions converge towards the discrete convection-diffusion limit with the same convergence rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin System Bessemoulin-Chatard, Marianne Mathis, Hélène Numerical Analysis This paper deals with the diffusive limit of the Jin and Xin model and its approximation by an asymptotic preserving finite volume scheme. At the continuous level, we determine a convergence rate to the diffusive limit by means of a relative entropy method. Considering a semi-discrete approximation (discrete in space and continuous in time), we adapt the method to this semi-discrete framework and establish that the approximated solutions converge towards the discrete convection-diffusion limit with the same convergence rate. |
| title | Relative Entropy for the Numerical Diffusive Limit of the Linear Jin-Xin System |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.03268 |