Error Estimates and Blow-Up Analysis of a Finite-Element Approximation for the Parabolic-Elliptic Keller-Segel System
Year: 2022
Author: Wenbin Chen, Qianqian Liu, Jie Shen
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 275–298
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20481
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 275–298
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Parabolic-elliptic systems finite element method error estimates finite-time blowup.