Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces
Year: 2017
Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 718–747
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2016-0029
Communications in Computational Physics, Vol. 21 (2017), Iss. 3 : pp. 718–747
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
-
Understanding the dual effects of linear cross-diffusion and geometry on reaction–diffusion systems for pattern formation
Sarfaraz, Wakil | Yigit, Gulsemay | Barreira, Raquel | Remaki, Lakhdar | Alhazmi, Muflih | Madzvamuse, AnotidaChaos, Solitons & Fractals, Vol. 186 (2024), Iss. P.115295
https://doi.org/10.1016/j.chaos.2024.115295 [Citations: 0] -
A domain-dependent stability analysis of reaction–diffusion systems with linear cross-diffusion on circular domains
Yigit, Gulsemay | Sarfaraz, Wakil | Barreira, Raquel | Madzvamuse, AnotidaNonlinear Analysis: Real World Applications, Vol. 77 (2024), Iss. P.104042
https://doi.org/10.1016/j.nonrwa.2023.104042 [Citations: 1] -
A surface moving mesh method based on equidistribution and alignment
Kolasinski, Avary | Huang, WeizhangJournal of Computational Physics, Vol. 403 (2020), Iss. P.109097
https://doi.org/10.1016/j.jcp.2019.109097 [Citations: 2] -
Numerical Preservation of Velocity Induced Invariant Regions for Reaction–Diffusion Systems on Evolving Surfaces
Frittelli, Massimo | Madzvamuse, Anotida | Sgura, Ivonne | Venkataraman, ChandrasekharJournal of Scientific Computing, Vol. 77 (2018), Iss. 2 P.971
https://doi.org/10.1007/s10915-018-0741-7 [Citations: 10] -
Analysis and Simulations of Coupled Bulk-surface Reaction-Diffusion Systems on Exponentially Evolving Volumes
Madzvamuse, A. | Chung, A. H. | Morozov, A. | Ptashnyk, M. | Volpert, V.Mathematical Modelling of Natural Phenomena, Vol. 11 (2016), Iss. 5 P.4
https://doi.org/10.1051/mmnp/201611502 [Citations: 4] -
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds
Krause, Andrew L. | Ellis, Meredith A. | Van Gorder, Robert A.Bulletin of Mathematical Biology, Vol. 81 (2019), Iss. 3 P.759
https://doi.org/10.1007/s11538-018-0535-y [Citations: 40] -
Mechanisms of cell polarization
Rappel, Wouter-Jan | Edelstein-Keshet, LeahCurrent Opinion in Systems Biology, Vol. 3 (2017), Iss. P.43
https://doi.org/10.1016/j.coisb.2017.03.005 [Citations: 101]