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Provably unconditionally stable, second-order time-accurate, mixed variational methods for phase-field models. (English) Zbl 1419.76439

Summary: 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.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T99 Multiphase and multicomponent flows
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