We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and total pressure, and the elasticity equations are written in the displacement-pressure formulation. The construction of the virtual element scheme does not require Lagrange multipliers to impose the transmission conditions (continuity of displacement and total traction, and no-flux for the fluid) on the interface. We show the stability and convergence of the virtual element method for different polynomial degrees, and the error bounds are robust with respect to delicate model parameters (such as Lame constants, permeability, and storativity coefficient). Finally, we provide numerical examples that illustrate the properties of the scheme.

翻译：本文提出、分析并实现了一种用于界面孔隙弹性-弹性固结问题的虚拟单元离散化方法。时变孔隙弹性方程的公式化表述使用了位移、流体压力和总压力，而弹性方程则采用位移-压力形式进行描述。虚拟单元方案的构建无需引入拉格朗日乘子来施加界面上的传递条件（位移和总牵引力的连续性以及流体的无通量条件）。我们证明了不同多项式阶次下虚拟单元法的稳定性和收敛性，其误差界相对于关键模型参数（如拉梅常数、渗透率和储水系数）具有鲁棒性。最后，我们提供了数值算例以说明该方案的性质。