An adaptive finite element Moreau-Yosida based solver for a non-smooth Cahn-Hilliard problem
Please always quote using this URN:urn:nbn:de:0296-matheon-6589
- 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.
Author: | Michael Hintermüller, Michael Hinze, Hicham M. Tber |
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URN: | urn:nbn:de:0296-matheon-6589 |
Referee: | Carsten Carstensen |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/10/29 |
Release Date: | 2009/10/15 |
Tag: | |
Institute: | Research Center Matheon |
Humboldt-Universität zu Berlin | |
MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx] / 49M15 Newton-type methods |
65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K10 Optimization and variational techniques [See also 49Mxx, 93B40] | |
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Preprint Number: | 670 |