三元Cahn-Hilliard相场模型的无条件能量稳定的Galerkin有限元格式OA

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.