  Biot's equations of poroelasticity contain a parabolic system for the
evolution of the pressure, which is coupled with a quasi-stationary equation
for the stress tensor. Thus, it is natural to extend the existing work on
isogeometric space-time methods to this more advanced framework of a partial
differential-algebraic equation (PDAE). A space-time approach based on finite
elements has already been introduced. But we present a new weak formulation in
space and time that is appropriate for an isogeometric discretization and
analyze the convergence properties. Our approach is based on a single
variational problem and hence differs from the iterative space-time schemes
considered so far. Further, it enables high-order convergence. Numerical
experiments that have been carried out confirm the theoretical findings.
