  The finite-size effect in gravitational microlensing provides a possibility
to measure the limb darkening of distant stars. We use the Finite Element
Method (FEM) as an inversion tool for discretization and inversion of the
magnification-limb darkening integral equation. This method makes no explicit
assumption about the shape of the brightness profile more than the flatness of
the profile near the center of the stellar disk. From the simulation, we
investigate the accuracy and stability of this method and we use regularization
techniques to stabilize it. Finally, we apply this method to the single lens,
high magnification transit events of OGLE-2004-BLG-254 (SAAO-I),
MOA-2007-BLG-233/OGLE-2007-BLG-302 (OGLE-I, MOA-R), MOA-2010-BLG-436 (MOA-R),
MOA-2011-BLG-93 (Canopus-V), MOA-2011-BLG-300/OGLE-2011-BLG-0990 (Pico-I) and
MOA-2011-BLG-325/OGLE-2011-BLG-1101 (LT-I) in which light curves have been
observed with a high cadence near the peak \citep{Ch}. The recovered intensity
profile of stars from our analysis for five light curves are consistent with
the linear limb darkening and two events with the square-root profiles. The
advantage of FEM is to extract limb darkening of stars without any assumption
about the limb darkening model.
