A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation

• Published in: Numerische Mathematik Vol. 128; no. 2; pp. 377 - 406
• Main Authors: Guan, Zhen, Wang, Cheng, Wise, Steven M
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2014
• Subjects: Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Simulation; Theoretical; 65M12; 65R20

In this paper we devise a first-order-in-time, second-order-in-space, convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation. The unconditional unique solvability, energy stability and ℓ ∞ ( 0 , T ; ℓ 4 ) stability of the scheme are established. Using the a-priori stabilities, we p...