Higher-order iterative decoupling for poroelasticity
For researchers solving coupled poroelasticity problems, this provides a theoretical framework to design higher-order decoupling schemes with controlled error, though the approach is incremental as it extends known BDF methods.
The authors introduce higher-order time discretization schemes (up to order 5) for iteratively decoupling elliptic-parabolic problems like poroelasticity, and show that convergence depends on the interplay between time step size and contraction parameters, with explicit quantification for error balancing. Numerical experiments validate the theory, including a 3D biomechanics example.
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.