Mixed variational potentials and inherent symmetries of the Cahn-Hilliard theory of diffusive phase separation

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 470; no. 2164; p. 20130641
• Main Authors: Miehe, C, Hildebrand, F E, Böger, L
• Format: Journal Article
• Language: English
• Published: England 08.04.2014
• Subjects: coupled problems; diffusion; phase separation; finite-element method; variational principles
• ISSN: 1364-5021
• DOI: 10.1098/rspa.2013.0641

This work shows that the Cahn-Hilliard theory of diffusive phase separation is related to an intrinsic that determines the rate of concentration and the chemical potential. The principle characterizes a canonically compact model structure, where the two balances involved for the species content and microforce appear as the Euler equations of a variational statement. The existence of the variational principle underlines an in the two-field representation of the Cahn-Hilliard theory. This can be exploited in the numerical implementation by the construction of time- and space-discrete , which fully determine the update problems of typical time-stepping procedures. The mixed variational principles provide the most fundamental approach to the finite-element solution of the Cahn-Hilliard equation based on basis functions, leading to monolithic of iterative update procedures based on a linearization of the nonlinear problem. They induce in a natural format the choice of for Newton-type iterative updates, providing a speed-up and reduction of data storage when compared with non-symmetric implementations. In this sense, the potentials developed are believed to be fundamental ingredients to a deeper understanding of the Cahn-Hilliard theory.