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格式。在每个时间步内，我们迭代求解流动方程与力学方程，并对压力变量引入额外的阻尼步骤。根据两方程耦合强度的不同，我们明确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规律。此外，我们将所提方法与著名的固定应力方案进行了比较。