  Within this paper, we introduce and analyze a novel time stepping scheme for
linear poroelasticity. In each time frame, we iteratively solve the flow and
mechanics equations with an additional damping step for the pressure variable.
Depending on the coupling strength of the two equations, we explicitly quantify
the needed number of inner iteration steps to guarantee first-order
convergence. Within a number of numerical experiments, we confirm the
theoretical results and study the dependence of inner iteration steps in terms
of the coupling strength. Moreover, we compare our method to the well-known
fixed-stress scheme.
