Finite element approximation of a degenerate Allen-Cahn/Cahn-Hilliard system

摘要

We consider a fully practical finite element approximation of an Allen-Cahn/Cahn-Hilliard system with a degenerate mobility and a logarithmic free energy. This system arises in the modeling of phase separation and ordering in binary alloys. In addition to showing well-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Finally, some numerical experiments are presented. [References: 12]