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Article

Gerardo-Giorda, Luca
Numerical approximation of density dependent diffusion in age-structured population dynamics. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 88-97
MSC: 65N12, 65N30, 92D25 | MR 3204433 | Zbl 1340.92046
Keywords:
finite elements; convergence; stability; parabolic problem
Summary:
We study a numerical method for the diffusion of an age-structured population in a spatial environment. We extend the method proposed in [2] for linear diffusion problem, to the nonlinear case, where the diffusion coefficients depend on the total population. We integrate separately the age and time variables by finite differences and we discretize the space variable by finite elements. We provide stability and convergence results and we illustrate our approach with some numerical result.
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