In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with small problem sizes which still achieve key features such as parameter-robustness, local mass conservation, and robust preconditionor construction. For this we combine a nonconforming finite element and the interior over-stabilized enriched Galerkin methods with a suitable stabilization term. Robust a priori error estimates and parameter-robust preconditioner construction are proved, and numerical results illustrate our theoretical findings.

翻译：本文提出了一种新的多孔弹性两场公式有限元离散方法，以弹性位移和孔隙压力作为主要变量。主要目标是开发一种问题规模小、同时具有参数鲁棒性、局部质量守恒和鲁棒预处理器构造等关键特性的数值方法。为此，我们将非协调有限元方法与内部过稳定富集Galerkin方法相结合，并引入合适的稳定化项。本文证明了先验误差估计的鲁棒性和参数鲁棒预处理器的构造，数值结果验证了我们的理论发现。