  We consider a poromechanics model including frictionless contact mechanics.
The resulting model consists of the Biot equations with contact boundary
conditions leading to a variational inequality modelling mechanical
deformations coupled to a linear parabolic flow equation. We propose a fully
discrete iterative scheme for solving this model. This scheme decoupled the
flow and mechanics equations and extends the fixed-stress splitting scheme for
the Biot equations. We use finite elements in space and a backward Euler
discretization in time. We show that the fixed stress split scheme is a
contraction.
