Communications on Pure and Applied Analysis (CPAA)

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

Pages: 339 - 364, Volume 11, Issue 1, January 2012      doi:10.3934/cpaa.2012.11.339

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Norikazu Saito - Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan (email)

Abstract: 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.

Keywords:  Finite-element method, error analysis, nonlinear parabolic system, chemotaxis.
Mathematics Subject Classification:  Primary: 65M60, 65M15; Secondary: 35K55.

Received: January 2010;      Revised: August 2010;      Available Online: September 2011.