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Tuncer_Madzvamuse_CiCP_2017-Accepted-Revised.pdf (6.01 MB)

Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces

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journal contribution
posted on 2023-06-09, 02:43 authored by Anotida Madzvamuse
The focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization which is ``logically'' rectangular. Furthermore, the surface is not approximated but described exactly through the projection. The surface evolution law is incorporated into the projection operator resulting in a time-dependent operator. The time-dependent projection operator is composed of the radial projection with a Lipschitz continuous mapping. The projection operator is used to generate the surface mesh whose connectivity remains constant during the evolution of the surface. To illustrate the methodology several numerical experiments are exhibited for different surface evolution laws such as uniform isotropic (linear, logistic and exponential), anisotropic, and concentration-driven. This numerical methodology allows us to study new reaction-kinetics that only give rise to patterning in the presence of surface evolution such as the activator-activator and short-range inhibition; long-range activation.

Funding

Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1

InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION; 642866 - InCeM

Coupling Geometric PDEs with Physics; ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149

Simons Foundation Fellow; Simons Foundation

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Communications in Computational Physics

ISSN

1815-2406

Publisher

Cambridge University Press

Issue

3

Volume

21

Page range

718-747

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Mathematics Applied to Biology Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2016-09-08

First Open Access (FOA) Date

2017-01-25

First Compliant Deposit (FCD) Date

2016-09-04