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The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces

The Stabilized Finite Element Method for the Cahn-Hilliard Phase-Field Model of Diblock Copolymers on Evolving Surfaces

Year:    2025

Author:    Lulu Liu, Xufeng Xiao, Xinlong Feng

Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 103–126

Abstract

This work focuses on the efficient numerical simulation of the Cahn-Hilliard phase-field model of diblock copolymers on evolving surfaces. The model integrates Cahn-Hilliard dynamic of diblock copolymers with partial differential equation on evolving surfaces, which has the property of geometric complexity, nonlinearity and mass conservation. In the numerical simulation, the space-time discretization of the proposed model is realized by the evolving surface finite element method. The stabilized semi-implicit approach is included in the framework of the evolving surface finite element method to produce a linear, stable, conserved and high-accurate scheme for long time numerical simulations. The stability analysis of the designed numerical method is established. Through several numerical experiments, the convergence and stability of the numerical method are investigated. In addition, spinodal decomposition is performed to research the mass evolution and dynamics of the Cahn-Hilliard model of diblock copolymers on different evolving surfaces.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2024-0033

Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 103–126

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Cahn-Hilliard model of diblock copolymers evolving surface finite element method stability analysis long time numerical simulations.

Author Details

Lulu Liu

Xufeng Xiao

Xinlong Feng