Blank, Luise and Butz, Martin and Garcke, Harald (2011) SOLVING THE CAHN-HILLIARD VARIATIONAL INEQUALITY WITH A SEMI-SMOOTH NEWTON METHOD. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 17 (4). pp. 931-954. ISSN 1292-8119,
Full text not available from this repository. (Request a copy)Abstract
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading to a discrete variational inequality of saddle point type in each time step. In each iteration of the primal-dual active set method a linearized system resulting from the discretization of two coupled elliptic equations which are defined on different sets has to be solved. We show local convergence of the primal-dual active set method and demonstrate its efficiency with several numerical simulations.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FINITE-ELEMENT APPROXIMATION; PATTERN MULTIFRONTAL METHOD; FREE-ENERGY; EQUATION; MODEL; Cahn-Hilliard equation; active-set methods; semi-smooth Newton methods; gradient flows; PDE-constraint optimization; saddle point structure |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke Mathematics > Prof. Dr. Luise Blank |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 May 2020 06:58 |
| Last Modified: | 28 May 2020 06:58 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20017 |
Actions (login required)
 |
View Item |
