In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different finite-element discretizations and illustrate how not only does such a stabilized scheme provide numerical solutions that are free of non-physical oscillations, but it also allows one to iterate the fluid and mechanics problems in a fashion similar to the well-known fixed-stress split method. The resulting solution method is convergent without the necessity for additional terms to stabilize the iteration. Finally, 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.

翻译：本文提出一种新的稳定化方法，旨在消除低渗透率和/或小时间步长条件下Biot多孔弹性模型压力近似中的伪振荡现象。我们考虑了不同的有限元离散格式，并证明该稳定化方案不仅能提供无物理振荡的数值解，还能以类似于经典固定应力分裂法的方式对流体与力学问题进行迭代求解。所得求解方法具有收敛性，且无需引入额外项来稳定迭代过程。最后，我们通过数值算例展示了该稳定化方法与迭代求解器对模型物理参数和离散化参数的鲁棒性。