Energy-Stable Predictor–Corrector Schemes for the Cahn–Hilliard Equation
Document Type
Article
Journal/Book Title/Conference
Journal of Computational and Applied Mathematics
Volume
376
Publisher
Elsevier BV * North-Holland
Publication Date
3-6-2020
Award Number
NSF, Division of Mathematical Sciences 1816783
Funder
NSF, Division of Mathematical Sciences
Abstract
In this paper, we construct a new class of predictor–corrector time-stepping schemes for the Cahn–Hilliard equation, which are linear, second-order accurate in time, unconditionally energy stable, and uniquely solvable. Then, we present the stability and error estimates of the semi-discrete numerical schemes for solving the Cahn–Hilliard equation with general nonlinear bulk potentials. The semi-discrete scheme is further discretized using the compact central finite difference method. Several numerical examples are shown to verify the theoretical results. In particular, the numerical simulations show that the predictor–corrector schemes reach the second-order convergence rate at relatively larger time-step sizes than the classical linear schemes. The numerical strategies and theoretical tools developed in this article could be readily applied to study other phase-field models or models that can be cast as gradient flow problems.
Recommended Citation
Zhang, Jun et al. “Energy-Stable Predictor–Corrector Schemes for the Cahn–Hilliard Equation.” Journal of Computational and Applied Mathematics 376.C (2020): n. pag. Web. doi:10.1016/j.cam.2020.112832.
