# Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 4, page 617-630
- ISSN: 0764-583X

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topMarrocco, Americo. "Numerical simulation of chemotactic bacteria aggregation via mixed finite elements." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 617-630. <http://eudml.org/doc/194181>.

@article{Marrocco2010,

abstract = {
We start from a mathematical model which describes the collective motion
of bacteria taking into account the underlying biochemistry. This model
was first introduced by Keller-Segel [13].
A new formulation of the system of partial differential equations is
obtained by the introduction of a new variable (this new variable is similar
to the quasi-Fermi level in the framework of semiconductor modelling).
This new system of P.D.E. is approximated via a mixed finite element technique.
The solution algorithm is then described and finally we give some
preliminary numerical results. Especially our method is well adapted to
compute the concentration of bacteria.
},

author = {Marrocco, Americo},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Biophysics; chemotaxis; numerical simulation; mixed finite element.; mixed finite element},

language = {eng},

month = {3},

number = {4},

pages = {617-630},

publisher = {EDP Sciences},

title = {Numerical simulation of chemotactic bacteria aggregation via mixed finite elements},

url = {http://eudml.org/doc/194181},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Marrocco, Americo

TI - Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 4

SP - 617

EP - 630

AB -
We start from a mathematical model which describes the collective motion
of bacteria taking into account the underlying biochemistry. This model
was first introduced by Keller-Segel [13].
A new formulation of the system of partial differential equations is
obtained by the introduction of a new variable (this new variable is similar
to the quasi-Fermi level in the framework of semiconductor modelling).
This new system of P.D.E. is approximated via a mixed finite element technique.
The solution algorithm is then described and finally we give some
preliminary numerical results. Especially our method is well adapted to
compute the concentration of bacteria.

LA - eng

KW - Biophysics; chemotaxis; numerical simulation; mixed finite element.; mixed finite element

UR - http://eudml.org/doc/194181

ER -

## References

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- F. Hecht and A. Marrocco, Mixed finite element simulation of heterojunction structures including a boundary layer model for the quasi-fermi levels. COMPEL13 (1994) 757-770.
- W. Jäger and S. Luckhaus, On explosion of solution to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc.239 (1992) 819-824.
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- A. Marrocco and Ph. Montarnal, Simulation des modèles energy-transport à l'aide des éléments finis mixtes. C.R. Acad. Sci. Paris I 323 (1996) 535-541.
- Ph. Montarnal, Modèles de transport d'énergie des semi-conducteurs, études asymptotiques et résolution par des éléments finis mixtes. Ph.D. thesis, Université Paris VI (octobre 1997).
- A. Marrocco, 2d simulation of chemotactic bacteria aggregation. Rapport de recherche 4667, INRIA (décembre 2002).

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