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

Norikazu Saito

doi:10.3934/cpaa.2012.11.339

Article Contents

2012, Volume 11, Issue 1: 339-364. Doi: 10.3934/cpaa.2012.11.339 open access

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

Norikazu Saito^1,

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

Received: December 31, 2009

Revised: July 31, 2010

Published: December 2011

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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.

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Mathematics Subject Classification: Primary: 65M60, 65M15; Secondary: 35K55.

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