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.