On a decoupled solver for Biot's model
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Single-phase flow problems on deformable porous media are modelled by means of the so-called Biot's model. Several challenges appear in the numerical solution of this model. On the one hand, it is important to choose appropriate discretization schemes that avoid the appearance of spurious oscillations in the pressure approximation when low permeabilities and/or small time steps are considered. On the other hand, the efficient solution of the large-sparse systems of equations arising after discretization also is challenging. In this work, for different finite element discretizations of Biot's model, we propose a new stabilized scheme that provides numerical solutions that are free of non-physical oscillations, and that, at the same time, allows us to iterate the fluid and mechanic problems in a convergent way to obtain the solution of the whole coupled system. We present numerical results illustrating the robust behavior of both the stabilization and iterative solver with respect to the physical and discretization parameters of the model.