Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation

• Published in: Applied mathematics and computation Vol. 419; p. 126880
• Main Authors: Li, Yaxiang, Wang, Jiangxing
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.04.2022
• Subjects: Cahn-Hilliard equation; Error analysis; Finite element method; Scalar auxiliary variable approach; Unconditional; Finite element method; Cahn-Hilliard equation; 65B99; Error analysis; Unconditional; Scalar auxiliary variable approach; 65N06
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2021.126880

•The proposed stabilized FEM-SAV scheme is linear, unconditional energy stable, and suit for general nonlinear potential.•The unconditional, optimal convergence of this fully-discrete stabilized FEM-SAV scheme is studied by using energy estimate. The proposed method can be used to analysis the unconditional convergence of fully discrete SAV based method for more complicated phase- field models and other nonlinear problems.•Numerical experiments are proposed to demonstrate the accuracy of the scheme. In this paper, we construct and analyze an energy stable scheme by combining stabilized scalar auxiliary variable (SAV) approach with finite element method (FEM) for the well-known Cahn-Hilliard equation. The unconditional energy stability and optimal error estimates of the numerical scheme are proved rigorously. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the accuracy of the proposed method.