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A moving mesh finite element method and its application to population dynamics

Watkins, A. (2017) A moving mesh finite element method and its application to population dynamics. PhD thesis, University of Reading

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The moving mesh finite element method (MMFEM) is a highly useful tool for the numerical solution of partial differential equations. In particular, for reaction-diffusion equations and multi-phase equations, the method provides the ability to track features of interest such as blow-up, the ability to track a free boundary, and the ability to model a dynamic interface between phases. This is achieved through a geometric conservation approach, whereby the integral of a suitable quantity is constant within a given patch of elements, but the footprint and location of those elements are dynamic. We apply the MMFEM to a variety of systems, including for the first time to various forms of the Lotka-Volterra competition equations. We derive a Lotka-Volterra based reaction-diffusion-aggregation system with two phases, representing spatially segregated species separated by a competitive interface. We model this system using the MMFEM, conserving an integral of population density within each patch of elements. We demonstrate its feasibility as a tool for ecological studies.

Item Type:Thesis (PhD)
Thesis Supervisor:Baines, M., Glaister, P. and Grindrod, P.
Thesis/Report Department:Department of Mathematics
Identification Number/DOI:
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:73372


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