A Flux-Corrected Finite Element Method for Chemotaxis Problems

An implicit flux-corrected transport (FCT) algorithm is developed for a class of chemotaxis models. The coefficients of the Galerkin finite element discretization are adjusted in such a way as to guarantee mass conservation and keep the cell density nonnegative. The numerical behaviour of the proposed high-resolution scheme is tested on the blow-up problem for a minimal chemotaxis model with singularities. It is also shown that the results for an Escherichia coli chemotaxis model are in good agreement with experimental data reported in the literature.