  In this work we analyze an optimized artificial fixed-stress iteration scheme
for the numerical approximation of the Biot system modelling fluid flow in
deformable porous media. The iteration is based on a prescribed constant
artificial volumetric mean total stress in the first half step. The
optimization comes through the adaptation of a numerical stabilization or
tuning parameter and aims at an acceleration of the iterations. The separated
subproblems of fluid flow, written as a mixed first order in space system, and
mechanical deformation are discretized by space-time finite element methods of
arbitrary order. Continuous and discontinuous discretizations of the time
variable are encountered. The convergence of the iteration schemes is proved
for the continuous and fully discrete case. The choice of the optimization
parameter is identified in the proofs of convergence of the iterations. The
analyses are illustrated and confirmed by numerical experiments.

Numerical Analysis