Linear relaxation schemes for the Allen-Cahn-type and Cahn-Hilliard-type phase field models

DOI10.1016/j.aml.2022.108477zbMath1505.65264OpenAlexW4307295572MaRDI QIDQ2106112

Maosheng Jiang, Jia Zhao

Publication date: 8 December 2022

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2022.108477

zbMATH Keywords

phase field modelsenergy stablegradient flow systemlinear relaxation technique

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Multiphase and multicomponent flows (76T99) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
• The scalar auxiliary variable (SAV) approach for gradient flows
• Energy-stable Runge-Kutta schemes for gradient flow models using the energy quadratization approach
• Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxation
• A revisit of the energy quadratization method with a relaxation technique
• A Relaxation Scheme for the Nonlinear Schrödinger Equation
• The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
• High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics

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