scholarly journals A Flux-Corrected Finite Element Method for Chemotaxis Problems

2010 ◽  
Vol 10 (2) ◽  
pp. 219-232 ◽  
Author(s):  
R. Strehl ◽  
A. Sokolov ◽  
D. Kuzmin ◽  
S. Turek
Keyword(s):  
Finite Element ◽  
Blow Up ◽  
Mass Conservation ◽  
Finite Element Discretization ◽  
Chemotaxis Model ◽  
Element Discretization ◽  
Galerkin Finite Element ◽  
Flux Corrected Transport ◽  
Chemotaxis Models ◽  
Good Agreement

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

A TRUNCATED FOURIER/FINITE ELEMENT DISCRETIZATION OF THE STOKES EQUATIONS IN AN AXISYMMETRIC DOMAIN

2006 ◽  
Vol 16 (02) ◽  
pp. 233-263 ◽  
Author(s):  
Z. BELHACHMI ◽  
C. BERNARDI ◽  
S. DEPARIS ◽  
F. HECHT
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Stokes Problem ◽  
A Priori ◽  
Three Dimensional ◽  
Angular Variable ◽  
A Posteriori ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Good Agreement

We consider the Stokes problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of this problem which combines Fourier truncation and finite element methods applied to each of the two-dimensional systems. We give the detailed a priori and a posteriori analyses of the discretization and present some numerical experiments which are in good agreement with the analysis.

Buckling of Force-Excited Liquid-Filled Shells

1991 ◽  
Vol 113 (3) ◽  
pp. 418-422 ◽  
Author(s):  
R. A. Uras ◽  
W. K. Liu
Keyword(s):  
Equation Of Motion ◽  
Dynamic Buckling ◽  
Modal Interaction ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Galerkin Finite Element ◽  
Modal Coupling ◽  
The Matrix ◽  
Good Agreement ◽  
Discretization Procedure

The matrix equation of motion for liquid-filled shells with a particular reference to the influence of ground excitation are derived through a Galerkin/finite element discretization procedure. The modal coupling among the various combinations of axial and circumferential modes are identified. The equations for the dynamic buckling analysis of liquid-filled shells are presented. The buckling criteria of liquid-filled shells subjected to horizontal ground excitation are established. A comparison to available experimental results gives strikingly good agreement. The importance of modal interaction in the axial as well as circumferential directions is also demonstrated. This provides guidelines for a better understanding of dynamic buckling of liquid-filled shells.

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