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

Authors:
Hector Gomez;Thomas J. R. Hughes
Affiliations:
Group of Numerical Methods in Engineering, University of A Coruña, Department of Mathematical Methods, Campus de Elviña, s/n 15192 A Coruña, Spain;Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station C0200, 201 E. 24th Street, Austin, TX 78712, United States
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

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.