  In this paper we present a discontinuous Galerkin finite element method for
the solution of the transient Stokes equations on moving domains. For the
discretization we use an interior penalty Galerkin approach in space, and an
upwind technique in time. The method is based on a decomposition of the
space-time cylinder into finite elements. Our focus lies on three-dimensional
moving geometries, thus we need to triangulate four dimensional objects. For
this we will present an algorithm to generate $d+1$-dimensional simplex
space-time meshes and we show under natural assumptions that the resulting
space-time meshes are admissible. Further we will show how one can generate a
four-dimensional object resolving the domain movement. First numerical results
for the transient Stokes equations on triangulations generated with the newly
developed meshing algorithm are presented.
