TY - GEN A1 - Hintermüller, Michael A1 - Hinze, Michael A1 - Tber, Hicham M. T1 - An adaptive finite element Moreau-Yosida based solver for a non-smooth Cahn-Hilliard problem N2 - 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 discretised 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. KW - adaptive finite element method KW - Cahn-Hilliard system KW - constrained optimal control KW - phase separation KW - semismooth Newton KW - variational inequality Y1 - 2009 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/658 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-6589 ER -