Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models

• Published in: Journal of computational physics Vol. 230; no. 13; pp. 5310 - 5327
• Main Authors: Gomez, Hector, Hughes, Thomas J.R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 10-06-2011; Elsevier
• Subjects: Cahn–Hilliard; Computational techniques; Discretization; Exact sciences and technology; Free energy; Mathematical analysis; Mathematical methods in physics; Mathematical models; Mixed finite element; Nonlinear stability; Phase-field; Physics; Robustness; Stability; Time integration; Variational methods; Nonlinear stability; Phase-field; Mixed finite element; Time integration; Cahn–Hilliard; Second order; Variational methods; Free energy; Calculation methods; Finite element method; Algorithms; Discretization; Dynamics; Cahn Hilliard equation; Models; Calculation; Cahn-Hilliard
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2011.03.033

We introduce provably unconditionally stable mixed variational methods for phase-field models. Our formulation is based on a mixed finite element method for space discretization and a new second-order accurate time integration algorithm. The fully-discrete formulation inherits the main characteristics of conserved phase dynamics, namely, mass conservation and nonlinear stability with respect to the free energy. We illustrate the theory with the Cahn–Hilliard equation, but our method may be applied to other phase-field models. We also propose an adaptive time-stepping version of the new time integration method. We present some numerical examples that show the accuracy, stability and robustness of the new method.