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Volume 19, Issue 2-3
Error Estimates and Blow-Up Analysis of a Finite-Element Approximation for the Parabolic-Elliptic Keller-Segel System

Wenbin Chen, Qianqian Liu & Jie Shen

Int. J. Numer. Anal. Mod., 19 (2022), pp. 275-298.

Published online: 2022-04

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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.

  • Keywords

Parabolic-elliptic systems, finite element method, error estimates, finite-time blowup.

  • AMS Subject Headings

65M12, 35K61, 35K55, 92C17

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wbchen@fudan.edu.cn (Wenbin Chen)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-19-275, author = {Chen , WenbinLiu , Qianqian and Shen , Jie}, title = {Error Estimates and Blow-Up Analysis of a Finite-Element Approximation for the Parabolic-Elliptic Keller-Segel System }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20481.html} }
TY - JOUR T1 - Error Estimates and Blow-Up Analysis of a Finite-Element Approximation for the Parabolic-Elliptic Keller-Segel System AU - Chen , Wenbin AU - Liu , Qianqian AU - Shen , Jie JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 275 EP - 298 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20481.html KW - Parabolic-elliptic systems, finite element method, error estimates, finite-time blowup. AB -

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.

Chen , WenbinLiu , Qianqian and Shen , Jie. (2022). Error Estimates and Blow-Up Analysis of a Finite-Element Approximation for the Parabolic-Elliptic Keller-Segel System . International Journal of Numerical Analysis and Modeling. 19 (2-3). 275-298. doi:
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