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

Research

Computational & Applied Math Seminar

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

Speaker: Wenbin CHEN (Fudan University)
Time: Dec 15, 2021, 09:30-10:30
Location: Tencent Meeting ID 267-358-575

Abstract

The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, a new fully discrete scheme for this model was proposed by Shen and Xu, mass conservation, positivity and energy decay were proved for the proposed scheme, which are important properties of the original system.

Here 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. The work is with Qianqian Liu and Jie Shen.