A moving mesh finite element method and its application to population dynamics
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...
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ndltd-bl.uk-oai-ethos.bl.uk-7293462019-03-05T15:45:09ZA moving mesh finite element method and its application to population dynamicsWatkins, Anna2017The 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.510University of Readinghttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729346http://centaur.reading.ac.uk/73372/Electronic Thesis or Dissertation |
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510 Watkins, Anna A moving mesh finite element method and its application to population dynamics |
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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. |
author |
Watkins, Anna |
author_facet |
Watkins, Anna |
author_sort |
Watkins, Anna |
title |
A moving mesh finite element method and its application to population dynamics |
title_short |
A moving mesh finite element method and its application to population dynamics |
title_full |
A moving mesh finite element method and its application to population dynamics |
title_fullStr |
A moving mesh finite element method and its application to population dynamics |
title_full_unstemmed |
A moving mesh finite element method and its application to population dynamics |
title_sort |
moving mesh finite element method and its application to population dynamics |
publisher |
University of Reading |
publishDate |
2017 |
url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.729346 |
work_keys_str_mv |
AT watkinsanna amovingmeshfiniteelementmethodanditsapplicationtopopulationdynamics AT watkinsanna movingmeshfiniteelementmethodanditsapplicationtopopulationdynamics |
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1718996255785353216 |