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

Authors:
M. Hintermuller;M. Hinze;M. H. Tber
Affiliations:
Department of Mathematics, Humboldt-University of Berlin, Berlin, Germany;Department of Mathematics, University of Hamburg, Hamburg, Germany;Department of Mathematics and Scientific Computing, Karl-Franzens University, Graz, Austria
Venue:
Optimization Methods & Software - Advances in Shape and Topology Optimization: Theory, Numerics and New Applications Areas
Year:
2011

Citing 0
Cited 3

Distributed Optimal Control of the Cahn-Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density

SIAM Journal on Control and Optimization
An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system

Journal of Computational Physics
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements

Journal of Computational Physics

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Abstract

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.