This paper is devoted to a new formulation which couples the weak Galerkin method and the finite element method for approximating solutions of the equations of quasi-static poroelasticity which model flow through elastic porous media. It is assumed that the permeability of the elastic matrix depends nonlinearly on the dilatation of the porous medium. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and the well-posedness of both the continuous and discrete three-field formulations is proved. Error estimates for the proposed numerical method are obtained. These show that the method is locking free . Numerical experiments presented further demonstrate the accuracy and the locking free characteristic of the proposed numerical method.

本文致力于一种新的公式，该公式结合了弱Galerkin方法和有限元方法，用于近似模拟通过弹性多孔介质流动的准静态多孔弹性方程组的解。假设弹性基质的渗透率非线性地取决于多孔介质的膨胀。该系统的稳态版本根据位移，压力和体积应力进行了重铸，并证明了连续和离散三场公式的适定性。获得了所提出数值方法的误差估计。这些表明该方法是免费的。提出的数值实验进一步证明了所提出数值方法的准确性和无锁定特性。