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Zbl 1172.92311
Efendiev, Messoud; Nakaguchi, Etsushi; Wendland, Wolfgang L.
Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme. (English)
[J] J. Math. Anal. Appl. 358, No. 1, 136-147 (2009). ISSN 0022-247X

Summary: We continue our systematic study of the dimension estimate of the global attractors for chemotaxis-growth systems and their finite-element approximations [see Discrete Contin. Dyn. Syst. 2007, Suppl., 334--343 (2007; Zbl 1163.37396)]. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter.

MSC 2000:: *92C17 Cell movement
65N30 Finite numerical methods (BVP of PDE)
37N25 Dynamical systems in biology
35Q80 Appl. of PDE in areas other than physics

Keywords: dimension of global attractor; finite-element approximation; upwind scheme; nonnegativity of solutions; chemotaxis-growth system

Citations: Zbl 1163.37396

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