A new strategy based on the space-time finite element notion 
is proposed for computations involving moving boundaries and 
interfaces. In the deforming-spatial-domain/ space-time (DSD/ST)
procedure the variational formulation of a problem is written 
over its space-time domain, and therefore the deformation of 
the spatial domain with respect to time is taken into account 
automatically. Because a space-time mesh is generated over the 
space-time domain of the problem, within each time step, the 
boundary (or interface) nodes move with the boundary (or interface). 
Whether the motion of the boundary is specified or not, the strategy 
is nearly the same. If the motion of the boundary is unknown 
then the boundary nodes move as defined by the other unknowns 
at the boundary (such as the velocity or the displacement). At 
the end of each time step a new spatial mesh can be generated 
over the current spatial domain. For computational feasibility 
the finite element interpolation functions are chosen to be 
discontinuous in time, and the fully discretized equations are
solved one space-time slab at a time.