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 the 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：针对多孔弹性等椭圆-抛物线问题的迭代解耦，我们引入了基于向后微分公式的时间离散格式，最高阶数可达5阶。其分析结合了不动点迭代技术与时间离散收敛性分析。主要结果表明，收敛性取决于时间步长与迭代格式压缩参数之间的相互作用。此外，本文对此关联进行了显式量化，从而能够平衡各误差分量。多个数值实验验证并阐释了理论结果，包括一个来自生物力学的三维算例。