We propose a novel time stepping method for linear poroelasticity by extending a recent iterative decoupling approach to the second-order case. This results in a two-step scheme with an inner iteration and a relaxation step. We prove second-order convergence for a prescribed number of inner iteration steps, only depending on the coupling strength of the elastic and the flow equation. The efficiency of the scheme is illustrated by a number of numerical experiments, including a simulation of three-dimensional brain tissue.

翻译：我们通过将近期提出的迭代解耦方法推广至二阶情形，提出了一种适用于线性孔隙弹性的新型时间步进格式。该格式包含内迭代和松弛步骤的两步方案。我们证明，在预设的内迭代步数下（该步数仅取决于弹性方程与流动方程的耦合强度），格式具有二阶收敛性。通过包括三维脑组织模拟在内的数值实验，验证了该格式的有效性。