Year: 2025
Author: Michal Beneš, Miroslav Kolář, Jan Magnus Sischka, Axel Voigt
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 5 : pp. 603–613
Abstract
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.
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/ijnam2025-1026
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 5 : pp. 603–613
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Motion by geodesic curvature surface Allen-Cahn equation de Gennes-Cahn-Hilliard energy matched asymptotic expansion graph formulation.