A posteriori existence for the Keller-Segel model via a finite volume scheme
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915506626232320 |
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| author | Hoffmann, Marc Giesselmann, Jan |
| author_facet | Hoffmann, Marc Giesselmann, Jan |
| contents | We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(Ω))$- and $L^2(0,T;H^1(Ω))$-norm and exhibit linear convergence in the mesh size, as observed in numerical experiments. Crucially, we show that as long as the condition of the error estimate is satisfied a weak solution exits. This means, as long as the numerical solution has good properties, we can rigorously infer existence of an exact solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A posteriori existence for the Keller-Segel model via a finite volume scheme Hoffmann, Marc Giesselmann, Jan Numerical Analysis We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(Ω))$- and $L^2(0,T;H^1(Ω))$-norm and exhibit linear convergence in the mesh size, as observed in numerical experiments. Crucially, we show that as long as the condition of the error estimate is satisfied a weak solution exits. This means, as long as the numerical solution has good properties, we can rigorously infer existence of an exact solution. |
| title | A posteriori existence for the Keller-Segel model via a finite volume scheme |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.17710 |