We focus on a three-field (displacement-velocity-pressure) stabilized mixed method for poroelasticity based on piecewise trilinear (Q_1), lowest order Raviart-Thomas (RTo), and piecewise constant (Po) approximations for displacement, Darcy's velocity and fluid pore pressure, respectively. Since the selected discrete spaces do not intrinsically satisfy the inf-sup condition in the undrained/in-compressible limit, we propose a stabilization strategy based on local pressure jumps. Then, we focus on the efficient solution of the stabilized formulation by a block preconditioned Krylov method. Robustness and efficiency of the proposed approach are demonstrated in two sets of numerical experiments.
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