  We present a parametric finite element approximation of two-phase flow. This
free boundary problem is given by the Stokes equations in the two phases, which
are coupled via jump conditions across the interface. Using a novel variational
formulation for the interface evolution gives rise to a natural discretization
of the mean curvature of the interface. In addition, the mesh quality of the
parametric approximation of the interface does not deteriorate, in general,
over time; and an equidistribution property can be shown for a semidiscrete
continuous-in-time variant of our scheme in two space dimensions. Moreover, on
using a simple XFEM pressure space enrichment, we obtain exact volume
conservation for the two phase regions. Furthermore, our fully discrete finite
element approximation can be shown to be unconditionally stable. We demonstrate
the applicability of our method with some numerical results which, in
particular, demonstrate that spurious velocities can be avoided in the
classical test cases.
