A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911912183201792 |
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| author | Giesselmann, Jan Kwon, Kiwoong |
| author_facet | Giesselmann, Jan Kwon, Kiwoong |
| contents | We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity needs to be small enough - which can be ensured by mesh refinement - and optimal in the sense that the error estimator decays with the same order as the error under mesh refinement. A specific feature of our error estimator is that it can be used to prove existence of a weak solution up to a certain time based on numerical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_09036 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model Giesselmann, Jan Kwon, Kiwoong Numerical Analysis 65M50, 65M08, 35K40 We provide a posteriori error estimates for a discontinuous Galerkin scheme for the parabolic-elliptic Keller-Segel system in 2 or 3 space dimensions. The estimates are conditional, in the sense that an a posteriori computable quantity needs to be small enough - which can be ensured by mesh refinement - and optimal in the sense that the error estimator decays with the same order as the error under mesh refinement. A specific feature of our error estimator is that it can be used to prove existence of a weak solution up to a certain time based on numerical results. |
| title | A posteriori error control for a Discontinuous Galerkin approximation of a Keller-Segel model |
| topic | Numerical Analysis 65M50, 65M08, 35K40 |
| url | https://arxiv.org/abs/2309.09036 |