Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 13, Pages 5310-5327Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.03.033
Keywords
Nonlinear stability; Phase-field; Mixed finite element; Time integration; Cahn-Hilliard
Funding
- Xunta de Galicia [09REM005118PR, 09MDS00718PR]
- Ministerio de Ciencia a Innovacin [DPI2009-14546-C02-01, DPI2010-16496]
- FEDER
- Universidad de A Coruna
- Office of Naval Research [N00014-08-1-0992]
- Institute for Computational Engineering and Sciences
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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. (C) 2011 Elsevier Inc. All rights reserved.
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