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arXiv · 2212.07655

Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system

Wenbin Chen·Qianqian Liu·Jie Shen
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Abstract

The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, a new fully discrete scheme for this model was proposed in [46], mass conservation, positivity and energy decay were proved for the proposed scheme, which are important properties of the original system. In this paper, we establish the error estimates of this scheme. Then, based on the error estimates, we derive the finite-time blowup of nonradial numerical solutions under some conditions on the mass and the moment of the initial data.

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Wenbin Chen, Qianqian Liu, Jie Shen. 2022-12-15. Error estimates and blow-up analysis of a finite-element approximation for the parabolic-elliptic Keller-Segel system. https://arxiv.org/abs/2212.07655

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