I will present some recent results on error analysis of
fully discrete finite element approximations for
the Allen-Cahn equation, the Cahn-Hilliard equation,
and the phase field model. Moreover, I will explain
how these new error estimates are used to establish
the convergence of the numerical
solutions (including interfaces) to the solutions
of three well-known free boundary
problems, namely, the mean curvature flow, the
Hele-Shaw/Mullins-Sekerka problem,
and the Stefan problem with or without surface
tension and surface kinetics.
This is a joint work with Andreas Prohl of the
University of Kiel of Germany.
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