  A new approach is developed to derive an analytical form for mobility
corrections in phase-field models for pure material solidification. Similar to
the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove
systematic errors in the kinetics of phase-field models that arise due to the
diffusivity of the interface. The new approach harnesses local information
within the diffuse interface instead of an expansion within the interface
peclet number $p_e=\eta/\delta$, the ratio of diffuse interface thickness to
diffusion length. Therefore it has no need for an approximation of $p_e$ being
small. This results in a broader range of applicability of the approach for
higher $p_e$.
