Journal
OPTIMIZATION METHODS & SOFTWARE
Volume 26, Issue 4-5, Pages 777-811Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556788.2010.549230
Keywords
Cahn-Hilliard model; double obstacle free energy; Moreau-Yosida regularization technique; semi-smooth Newton method; adaptive finite elements
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Funding
- Austrian Ministry of Science and Research
- Austrian Science Fund FWF [Y305]
- DFG Research Center MATHEON
- DFG [SPP1253]
- Austrian Science Fund (FWF) [F 3204, Y 305] Funding Source: researchfish
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An adaptive finite-element semi-smooth Newton solver for the Cahn-Hilliard model with double obstacle free energy is proposed. For this purpose, the governing system is discretized in time using a semi-implicit scheme, and the resulting time-discrete system is formulated as an optimal control problem with pointwise constraints on the control. For the numerical solution of the optimal control problem, we propose a function space-based algorithm which combines a Moreau-Yosida regularization technique for handling the control constraints with a semi-smooth Newton method for solving the optimality systems of the resulting sub-problems. Further, for the discretization in space and in connection with the proposed algorithm, an adaptive finite-element method is considered. The performance of the overall algorithm is illustrated by numerical experiments.
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