  We propose a novel time stepping method for linear poroelasticity by
extending a recent iterative decoupling approach to the second-order case. This
results in a two-step scheme with an inner iteration and a relaxation step. We
prove second-order convergence for a prescribed number of inner iteration
steps, only depending on the coupling strength of the elastic and the flow
equation. The efficiency of the scheme is illustrated by a number of numerical
experiments, including a simulation of three-dimensional brain tissue.
