We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves the computational efficiency. The construction and the convergence proof are based on the connection to a differential equation with two time delays, namely one and two times the step size. Numerical experiments confirm the theoretical results and indicate the applicability to higher-order schemes.

翻译：我们针对满足弱耦合条件的线性孔隙弹性问题，提出一种二阶半显式时间推进格式。其中“半显式”意指每步需要求解的系统实现解耦，从而提升计算效率。该格式的构造与收敛性证明基于其与含两个时滞（即步长的一倍和两倍）的微分方程的内在关联。数值实验验证了理论结果，并表明该方法可拓展至高阶格式。