  We consider the dynamic Biot model describing the interaction between fluid
flow and solid deformation including wave propagation phenomena in both the
liquid and solid phases of a saturated porous medium. The model couples a
hyperbolic equation for momentum balance to a second-order in time dynamic
Darcy law and a parabolic equation for the balance of mass and is here
considered in three-field formulation with the displacement of the elastic
matrix, the fluid velocity, and the fluid pressure being the physical fields of
interest. A family of variational space-time finite element methods is proposed
that combines a continuous-in-time Galerkin ansatz of arbitrary polynomial
degree with inf-sup stable $H(\rm{div})$-conforming approximations of
discontinuous Galerkin (DG) type in case of the displacement and a mixed
approximation of the flux, its time derivative and the pressure field. We prove
error estimates in a combined energy norm as well as $L^2$~error estimates in
space for the individual fields for both maximum and $L^2$ norm in time which
are optimal for the displacement and pressure approximations.
