  In this paper, we propose a multiphysics mixed finite element method with
Nitsche's technique for Stokes-poroelasticity problem. Firstly, we present a
multiphysics reformulation of poroelasticity part of the original problem by
introducing two pseudo-pressures to reveal the underlying deformation and
diffusion multi physical processes in the Stokes-poroelasticity problem. Then,
we prove the existence and uniqueness of weak solution of the reformulated and
original problem. And we use Nitsche's technique to approximate the coupling
condition at the interface to propose a loosely-coupled time-stepping method --
multiphysics mixed finite element method for space variables, and we decouple
the reformulated problem into three sub-problems at each time step -- a Stokes
problem, a generalized Stokes problem and a mixed diffusion problem. Also, we
give the stability analysis and error estimates of the loosely-coupled
time-stepping method.
