Tuncer_Madzvamuse_CiCP_2017-Accepted-Revised.pdf (6.01 MB)
Download fileProjected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces
journal contribution
posted on 2023-06-09, 02:43 authored by Anotida MadzvamuseThe 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 PhysicsISSN
1815-2406Publisher
Cambridge University PressExternal DOI
Issue
3Volume
21Page range
718-747Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Mathematics Applied to Biology Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes