American Institute of Mathematical Sciences

January  2012, 11(1): 339-364. doi: 10.3934/cpaa.2012.11.339

Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis

 1 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan

Received  January 2010 Revised  August 2010 Published  September 2011

We are concerned with the finite-element approximation for the Keller-Segel system that describes the aggregation of slime molds resulting from their chemotactic features. The scheme makes use of a semi-implicit time discretization with a time-increment control and Baba-Tabata's conservative upwind finite-element approximation in order to realize the positivity and mass conservation properties. The main aim is to present error analysis that is an application of the discrete version of the analytical semigroup theory.
Citation: Norikazu Saito. Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis. Communications on Pure & Applied Analysis, 2012, 11 (1) : 339-364. doi: 10.3934/cpaa.2012.11.339
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