An adaptive finite-element Moreau-Yosida-based solver for a non-smooth Cahn-Hilliard problem

作者：Hintermueller M; Hinze M; Tber M H^*

来源：Optimization Methods and Software, 2011, 26(4-5): 777-811.

DOI：10.1080/10556788.2010.549230

• Cahn-Hilliard model
• double obstacle free energy
• Moreau-Yosida regularization technique
• semi-smooth Newton method
• adaptive finite elements

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.

• 出版日期2011