an:05971708
Zbl 1366.74070
Hinterm??ller, M.; Hinze, M.; Tber, M. H.
An adaptive finite-element Moreau-Yosida-based solver for a non-smooth Cahn-Hilliard problem
EN
Optim. Methods Softw. 26, No. 4-5, 777-811 (2011).
00288926
2011
j
74S05 74N20 74M05
double obstacle free energy; Moreau-Yosida regularization technique; semi-smooth Newton method; optimal control
Summary: 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.