In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that is, a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. A new technique is used to get the existence and uniqueness of the solution of the reformulated model and a fully discrete nonlinear finite element method is proposed to solve the model numerically. The multiphysics finite element is used to get the discretization of the space variable and the backward Euler method is taken as the time-stepping method in the fully discrete case. Stability analysis and the error estimation are given for the fully discrete case and numerical test are taken to verify the theoretical results.

翻译：在本文中,我们研究了非线性孔径弹性模型与非线性应力-线性关系的数字算法。 通过使用变量替代, 原始问题可以重拟为一个新的混合流体流体-流体系统, 即与伪压力和其他伪压力字段扩散问题相关的非线性非线性传动矢量场的普遍的非线性传动问题。 使用了一种新技术来获得重塑模型解决方案的存在和独特性, 并提出了一个完全离散的非线性非线性有限元素方法来从数字上解析模型。 多物理性有限元素用来获得空间变量的离散化,而落后的 Euler 方法则在完全离散的情况下作为时间步骤法使用。 对完全离散的情况进行了稳定性分析和误差估计, 并用数字测试来核实理论结果 。