# American Institute of Mathematical Sciences

December  2013, 18(10): 2689-2704. doi: 10.3934/dcdsb.2013.18.2689

## Numerical simulation of chemotaxis models on stationary surfaces

 1 Institut für Angewandte Mathematik, TU Dortmund, 44227 Dortmund, Germany, Germany, Germany

Received  November 2012 Revised  April 2013 Published  October 2013

In this paper we present an implicit finite element method for a class of chemotaxis models, where a new linearized flux-corrected transport (FCT) algorithm is modified in such a way as to keep the density of on-surface living cells nonnegative. Level set techniques are adopted for an implicit description of the surface and for the numerical treatment of the corresponding system of partial differential equations. The presented scheme is able to deliver a robust and accurate solution for a large class of chemotaxis-driven models. The numerical behavior of the proposed scheme is tested on the blow-up model on a sphere and an ellipsoid and on the pattern-forming dynamics model of Escherichia coli on a sphere.
Citation: Andriy Sokolov, Robert Strehl, Stefan Turek. Numerical simulation of chemotaxis models on stationary surfaces. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2689-2704. doi: 10.3934/dcdsb.2013.18.2689
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