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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.13067 |
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| _version_ | 1866909397061468160 |
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| author | Fang, Zexiong Cheng, Qing |
| author_facet | Fang, Zexiong Cheng, Qing |
| contents | In this paper, we improve the original Lagrange multiplier approach \cite{ChSh22,ChSh_II22} and introduce a new energy correction approach to construct a class of robust, positivity/bound-preserving, mass conserving and energy dissipative schemes for Keller-Segel equations which only need to solve several linear Poisson like equations. To be more specific, we use a predictor-corrector approach to construct a class of positivity/bound-preserving and mass conserving schemes which can be implemented with negligible cost. Then a energy correction step is introduced to construct schemes which are also energy dissipative, in addition to positivity/bound-preserving and mass conserving. This new approach is not restricted to any particular spatial discretization and can be combined with various time discretization to achieve high-order accuracy in time. We show stability results for mass-conservative, positivity/bound-preserving and energy dissipative schemes for two different Keller-Segel systems. A error analysis is presented for a second-order, bound-preserving, mass-conserving and energy dissipative scheme for the second-type of Keller-Segel equations. Ample numerical experiments are shown to validate the stability and accuracy of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new class of energy dissipative, mass conserving and positivity/bound-preserving schemes for Keller-Segel equations Fang, Zexiong Cheng, Qing Numerical Analysis In this paper, we improve the original Lagrange multiplier approach \cite{ChSh22,ChSh_II22} and introduce a new energy correction approach to construct a class of robust, positivity/bound-preserving, mass conserving and energy dissipative schemes for Keller-Segel equations which only need to solve several linear Poisson like equations. To be more specific, we use a predictor-corrector approach to construct a class of positivity/bound-preserving and mass conserving schemes which can be implemented with negligible cost. Then a energy correction step is introduced to construct schemes which are also energy dissipative, in addition to positivity/bound-preserving and mass conserving. This new approach is not restricted to any particular spatial discretization and can be combined with various time discretization to achieve high-order accuracy in time. We show stability results for mass-conservative, positivity/bound-preserving and energy dissipative schemes for two different Keller-Segel systems. A error analysis is presented for a second-order, bound-preserving, mass-conserving and energy dissipative scheme for the second-type of Keller-Segel equations. Ample numerical experiments are shown to validate the stability and accuracy of our approach. |
| title | A new class of energy dissipative, mass conserving and positivity/bound-preserving schemes for Keller-Segel equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.13067 |