@Article{IJNAM-22-603,
author = {Beneš , MichalKolář , MiroslavSischka , Jan Magnus and Voigt , Axel},
title = {Degenerate Area Preserving Surface Allen-Cahn Equation and Its Sharp Interface Limit},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {5},
pages = {603--613},
abstract = {<p style="text-align: justify;">We consider formal matched asymptotics to show the convergence of a degenerate
area preserving surface Allen-Cahn equation to its sharp interface limit of area preserving geodesic
curvature flow. The degeneracy results from a surface de Gennes-Cahn-Hilliard energy and turns
out to be essential to numerically resolve the dependency of the solution on geometric properties
of the surface. We experimentally demonstrate convergence of the numerical algorithm, which
considers a graph formulation, adaptive finite elements and a semi-implicit discretization in time,
and uses numerical solutions of the sharp interface limit, also considered in a graph formulation,
as benchmark solutions. The results provide the mathematical basis to explore the impact of
curvature on cells and their collective behaviour. This is essential to understand the physical
processes underlying morphogenesis.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1026},
url = {http://global-sci.org/intro/article_detail/ijnam/24078.html}
}