  In the recent paper [C. Lehrenfeld, A. Reusken, SIAM J. Num. Anal., 51
(2013)] a new finite element discretization method for a class of two-phase
mass transport problems is presented and analyzed. The transport problem
describes mass transport in a domain with an evolving interface. Across the
evolving interface a jump condition has to be satisfies. The discretization in
that paper is a space-time approach which combines a discontinuous Galerkin
(DG) technique (in time) with an extended finite element method (XFEM). Using
the Nitsche method the jump condition is enforced in a weak sense. While the
emphasis in that paper was on the analysis and one dimensional numerical
experiments the main contribution of this paper is the discussion of
implementation aspects for the spatially three dimensional case. As the
space-time interface is typically given only implicitly as the zero-level of a
level-set function, we construct a piecewise planar approximation of the
space-time interface. This discrete interface is used to divide the space-time
domain into its subdomains. An important component within this decomposition is
a new method for dividing four-dimensional prisms intersected by a piecewise
planar space-time interface into simplices. Such a subdivision algorithm is
necessary for numerical integration on the subdomains as well as on the
space-time interface. These numerical integrations are needed in the
implementation of the Nitsche XFEM-DG method in three space dimensions.
Corresponding numerical studies are presented and discussed.
