  We consider unsteady poroelasticity problem in fractured porous medium within
the classical Barenblatt double-porosity model. For numerical solution of
double-porosity poroelasticity problems we construct splitting schemes with
respect to physical processes, where transition to a new time level is
associated with solving separate problem for the displacements and fluid
pressures in pores and fractures. The stability of schemes is achieved by
switching to three-level explicit-implicit difference scheme with some of the
terms in the system of equations taken from the lower time level and by
choosing a weight parameter used as a regularization parameter. The
computational algorithm is based on the finite element approximation in space.
The investigation of stability of splitting schemes is based on the general
stability (well-posedness) theory of operator-difference schemes. A priori
estimates for proposed splitting schemes and the standard two-level scheme are
provided. The accuracy and stability of considered schemes are demonstrated by
numerical experiments.
