Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915179916165120 |
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| author | Huang, Xueling Goubet, Olivier Shen, Jie |
| author_facet | Huang, Xueling Goubet, Olivier Shen, Jie |
| contents | We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled, first-order scheme preserves unconditionally the important properties of Keller-Segel equations at the semi-discrete level, including the mass conservation and positivity preserving of the cell density, and the energy dissipation. We also establish optimal error estimates in $L^p$-norm $(1<p<\infty)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_01427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model Huang, Xueling Goubet, Olivier Shen, Jie Numerical Analysis We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled, first-order scheme preserves unconditionally the important properties of Keller-Segel equations at the semi-discrete level, including the mass conservation and positivity preserving of the cell density, and the energy dissipation. We also establish optimal error estimates in $L^p$-norm $(1<p<\infty)$. |
| title | Numerical analysis of a semi-implicit Euler scheme for the Keller-Segel model |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2503.01427 |