The discretization in space is taken care of by a standard finite element approximation for the problem in ϕ and an Interior Penalty Discontinuous Galerkin (IPDG) approximation for the one in Θ. The splitting scheme is based on an implicit discretization in time which allows a decoupling of the system in the sense that at each time step minimization problems in ϕ and Θ have to be solved successively.
The phase field model consists of a coupled system of evolutionary processes for the local degree of crystallinity ϕ and the orientation angle Θ one of them being of first order total variation flow type. Abstract: We consider a space–time adaptive splitting scheme for polycrystallization processes described by a two-field phase field model.
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