For the iterative decoupling of elliptic–parabolic problems such as poroelasticity, we introduce time discretization schemes up to order five 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.

对于椭圆-抛物线问题（如多孔弹性）的迭代解耦，我们根据向后微分公式引入了高达 5 阶的时间离散化方案。它的分析将定点迭代中已知的技术与时间离散化的收敛分析相结合。作为主要结果，我们表明收敛取决于时间步长和迭代方案收缩参数之间的相互作用。此外，这种连接被显式量化，从而可以平衡单个误差分量。几个数值实验说明并验证了理论结果，包括生物力学的三维示例。