  This paper is concerned with adaptive mesh refinement strategies for the
spatial discretization of parabolic problems with dynamic boundary conditions.
This includes the characterization of inf-sup stable discretization schemes for
a stationary model problem as a preliminary step. Based on an alternative
formulation of the system as a partial differential-algebraic equation, we
introduce a posteriori error estimators which allow local refinements as well
as a special treatment of the boundary. We prove reliability and efficiency of
the estimators and illustrate their performance in several numerical
experiments.
