  Elemental abundance effects in active coronae have eluded our understanding
for almost three decades, since the discovery of the First Ionization Potential
(FIP) effect on the sun. The goal of this paper is to monitor the same coronal
structures over a time interval of six days and resolve active regions on a
stellar corona through rotational modulation. We report on four iso-phase X-ray
spectroscopic observations of the RS CVn binary EI Eri with XMM-Newton, carried
out approximately every two days, to match the rotation period of EI Eri. We
present an analysis of the thermal and chemical structure of the Ei Eri corona
as it evolves over the six days. Although the corona is rather steady in its
temperature distribution, the emission measure and FIP bias both vary and seem
to be correlated. An active region, predating the beginning of the campaign,
repeatedly enters into our view at the same phase as it rotates from beyond the
stellar limb. As a result, the abundances tend slightly, but consistently, to
increase for high FIP elements (an inverse FIP effect) with phase. We estimate
the abundance increase of high FIP elements in the active region to be of ~75%
over the coronal mean. This observed fractionation of elements in an active
region on time scales of days provides circumstantial clues regarding the
element enrichment mechanism of non-flaring stellar coronae.
