  In this paper, we present the numerical solution of two-phase flow problems
of engineering significance with a space-time finite element method that allows
for local temporal refinement. Our basis is the method presented in [3], which
allows for arbitrary temporal refinement in preselected regions of the mesh. It
has been extended to adaptive temporal refinement that is governed by a
quantity that is part of the solution process, namely, the interface position
in two-phase flow. Due to local effects such as surface tension, jumps in
material properties, etc., the interface can, in general, be considered a
region that requires high flexibility and high resolution, both in space and in
time. The new method, which leads to tetrahedral (for 2D problems) and
pentatope (for 3D problems) meshes, offers an efficient yet accurate approach
to the underlying two-phase flow problems.
