Wang, B. (2024, June 24). Structure-preserving semi-convex-splitting numerical scheme for a Cahn-Hilliard cross-diffusion system in lymphangiogenesis [Poster Presentation]. Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations and Collective Behavior, Marseille, France.
E101 - Institut für Analysis und Scientific Computing
-
Date (published):
24-Jun-2024
-
Event name:
Frontiers in Interacting Particle Systems, Aggregation-Diffusion Equations and Collective Behavior
en
Event date:
24-Jun-2024 - 28-Jun-2024
-
Event place:
Marseille, France
-
Keywords:
Cahn–Hilliard equation; cross-diffusion systems; free energy; lymphangiogenesis; convex splitting; finite-element method; energy stability; existence of discrete solutions
en
Abstract:
A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn- Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equa- tions for the volume fraction of the fiber phase and solute concentration, modeling pre-patterning of lymphatic vessel morphology. The existence of discrete solutions is proved, and it is shown that the numerical scheme is energy stable up to stabilization, conserves the solute mass, and preserves the lower and upper bounds of the fiber phase fraction. Numerical experiments in two space dimensions using FreeFEM illustrate the phase segregation and pattern formation.
en
Project title:
Multikomponentensysteme mit unvollständiger Diffusion: P 33010-N (FWF - Österr. Wissenschaftsfonds) Emergente Netzwerkstrukturen und neuromorphische Anwendungen: 101018153 (European Commission)
