论文标题
具有非线性应力 - 应变关系的非线性毛弹性模型的多物理有限元法的最佳误差估计
Optimal error estimates of multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relations
论文作者
论文摘要
在本文中，我们研究了具有非线性应力 - 应变关系的非线性毛弹性模型的数值算法。通过使用可变替代，可以将原始问题重新针对新的耦合流体流体系统，即与伪压力相关的位移载体场的广义非线性Stokes问题以及其他伪压力场的扩散问题。一种新技术用于获得重新计算模型解决方案的存在和唯一性，并提出了完全离散的非线性有限元方法来数值求解该模型。多物理有限元用于获得空间变量的离散化，在完全离散的情况下，向后的Euler方法作为时间稳定方法。对完全离散的情况进行了稳定性分析和误差估计，并进行数值测试以验证理论结果。
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.
