浙江大学学报（理学版）2026，Vol.53Issue(4)：464-473,489,11.DOI:10.3785/1008-9497.25108
三元Cahn-Hilliard相场模型的无条件能量稳定的Galerkin有限元格式
An unconditionally energy-stable Galerkin finite element scheme for ternary Cahn-Hilliard phase-field models
摘要
Abstract
To address the challenges of high coupling,strong nonlinearity,and the difficulty in obtaining analytical solutions for ternary Cahn-Hilliard phase-field models,a finite element scheme combining the scalar auxiliary variable(SAV)approach with a stabilization technique is proposed,and its unconditionally energy stability is proved.First,a scalar auxiliary variable is introduced to reformulate the model,transforming the nonlinear free energy functional into a quadratic form of the scalar auxiliary variable.Then a numerical scheme is constructed by incorporating the stabilization technique.For temporal discretization,we employ the second-order backward differentiation formula(BDF2).For spatial discretization,we utilize the Galerkin finite element method with quadratic Lagrange elements to approximate the phase-field variables.This scheme can effectively handle complex geometries and boundary conditions,thereby enhancing computational accuracy.Numerical experiments validate that the proposed finite element scheme achieves second-order convergence in the L2-norm for temporal discretization,and yields third-order and second-order convergence in the L2-norm and H1-norm for spatial discretization,respectively.Quantitative analysis based on energy evolution curves further confirms that the scheme strictly preserves the energy dissipation law during long-time simulations.关键词
三元Cahn-Hilliard模型/能量稳定性/Galerkin有限元方法/稳定化SAV方法Key words
ternary Cahn-Hilliard model/energy stability/Galerkin finite element method/stabilized SAV method分类
数理科学引用本文复制引用
李琦,刘俊杰,赵安旭,李玉超..三元Cahn-Hilliard相场模型的无条件能量稳定的Galerkin有限元格式[J].浙江大学学报（理学版）,2026,53(4):464-473,489,11.基金项目
陕西数理基础科学研究项目(22JSQ021) （22JSQ021）
中国博士后科学基金项目(2023M730359). （2023M730359）
