We analyze a semi-explicit time discretization scheme of first order for poroelasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of the equations and, at the same time, linearizes the nonlinearity without the need of further inner iteration steps. Hence, the computational speed-up is twofold without a loss in the convergence rate. We prove optimal first-order error estimates by considering a related delay system and investigate the method numerically for different examples with various types of nonlinear displacement-permeability relations.

翻译：我们分析一种半显性的时间分解方案,即以非线性渗透性为主的孔径直线性第一顺序,条件是弹性模型和流动方程式的连接弱。该方法导致方程式脱钩,同时将非线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性线性系统。因此,计算速度是双倍,而不会在趋同率上损失。我们通过考虑一个相关的延迟系统和从数字上调查与非线性偏移-渗透性关系不同类型的不同实例的方法,证明第一线性差误差估计是最佳的。