In this work, we consider the coupled systems of linear unsteady partialdifferential equations, which arise in the modeling of poroelasticityprocesses. Stability estimates of weighted difference schemes for the coupledsystem of equations are presented. Approximation in space is based on thefinite element method. We construct splitting schemes and give some numericalcomparisons for typical poroelasticity problems. The results of numericalsimulation of a 3D problem are presented. Special attention is given to usinghight performance computing systems.
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