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An energy-stable time-integrator for phase-field models

Vignal, P.; Collier, N.; Dalcin, L.; Brown, Donald; Calo, V.M.

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P. Vignal

N. Collier

L. Dalcin

Donald Brown

V.M. Calo


We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.


Vignal, P., Collier, N., Dalcin, L., Brown, D., & Calo, V. (2017). An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering, 316,

Journal Article Type Article
Acceptance Date Dec 27, 2016
Online Publication Date Dec 27, 2016
Publication Date Apr 1, 2017
Deposit Date Mar 23, 2017
Publicly Available Date Mar 23, 2017
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 316
Keywords Phase-field models; PetIGA; High-order partial differential equation; Mixed finite elements; Isogeometric analysis; Time integration
Public URL
Publisher URL


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