Blank, Luise and Butz, Martin and Garcke, Harald
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method.
EASIM: Control, Optimisation and Calculus of Variations, E-first.
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.
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||Cahn-Hilliard equation; active-set methods; semi-smooth Newton methods; gradient flows; PDE-constraint optimization; saddle point structure|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||23 Mar 2010 08:26|
|Last Modified:||31 Jan 2014 06:30|