  In this work, we consider the coupled systems of linear unsteady partial
differential equations, which arise in the modeling of poroelasticity
processes. Stability estimates of weighted difference schemes for the coupled
system of equations are presented. Approximation in space is based on the
finite element method. We construct splitting schemes and give some numerical
comparisons for typical poroelasticity problems. The results of numerical
simulation of a 3D problem are presented. Special attention is given to using
hight performance computing systems.
