| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1685 - 1704 | |
| DOI | https://doi.org/10.1051/m2an/2025039 | |
| Published online | 26 June 2025 | |
A structure-preserving quasi-convex-splitting finite-element scheme for a Cahn–Hilliard cross-diffusion system in lymphangiogenesis
Institute of Analysis and Scientific Computing, TU Wien, Wiedner Hauptstraße 8–10, 1040 Vienna, Austria
* Corresponding author: boyi.wang@tuwien.ac.at; d2reborn@gmail.com
Received:
21
June
2024
Accepted:
20
May
2025
This work proposes and analyzes a finite-element convex-splitting scheme for a thermodynamically consistent Cahn–Hilliard cross-diffusion system modeling pre-patterning in lymphatic vessel morphology. The existence of discrete solutions for the proposed scheme is proved, and the scheme is shown to preserve energy stability, mass conservation, and the positivity of the fiber phase fraction. Numerical experiments are also presented for non-degenerate and degenerate models, including simulations that verify the analysis and illustrate pattern formation.
Mathematics Subject Classification: 65M12 / 65M60 / 92C37
Key words: Cross-diffusion systems / lymphangiogenesis / finite-element method / energy stability / existence of discrete solutions
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.