Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable. Depending on the coupling strength of the two equations, we explicitly quantify the needed number of inner iteration steps to guarantee first-order convergence. Within a number of numerical experiments, we confirm the theoretical results and study the dependence of inner iteration steps in terms of the coupling strength. Moreover, we compare our method to the well-known fixed-stress scheme.

翻译：本文提出并分析了一种用于线性孔隙弹性问题的新型时间步进方案。在每个时间步内，我们通过迭代求解流动方程和力学方程，并对压力变量增加一个额外阻尼步骤。根据两个方程的耦合强度，我们显式量化了保证一阶收敛所需的内迭代步数。通过一系列数值实验，我们验证了理论结果，并研究了内迭代步数随耦合强度的变化关系。此外，我们将本方法与经典的固定应力方案进行了比较。