For the iterative decoupling of elliptic-parabolic problems such as poroelasticity, we introduce time discretization schemes up to order $5$ based on the backward differentiation formulae. Its analysis combines techniques known from fixed-point iterations with the convergence analysis of the temporal discretization. As main result, we show that the convergence depends on the interplay between the time step size and the parameters for the contraction of the iterative scheme. Moreover, this connection is quantified explicitly, which allows for balancing the single error components. Several numerical experiments illustrate and validate the theoretical results, including a three-dimensional example from biomechanics.

翻译：针对孔隙弹性力学等椭圆-抛物型问题的迭代解耦，本文基于后向微分公式提出了最高达五阶的时间离散格式。该分析将不动点迭代的已知技术与时间离散的收敛性分析相结合。主要研究结果表明，收敛性取决于时间步长与迭代格式收缩参数之间的相互作用。此外，这种关联被显式量化，从而实现了对各误差分量的平衡控制。多个数值实验（包括生物力学中的三维算例）验证并阐释了理论结果。