@Article{CiCP-21-3,
author = {},
title = {Projected Finite Elements for Systems of Reaction-Diffusion Equations on Closed Evolving Spheroidal Surfaces},
journal = {Communications in Computational Physics},
year = {2017},
volume = {21},
number = {3},
pages = {718--747},
abstract = {<p style="text-align: justify;">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 &quot;logically&quot; 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0029},
url = {https://global-sci.com/article/80097/projected-finite-elements-for-systems-of-reaction-diffusion-equations-on-closed-evolving-spheroidal-surfaces}
}