Higher-Order Iterative Decoupling for Poroelasticity
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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. For the analysis, we combine 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. We then discuss the numerical implementation details including suitable choices for pre-conditioning and error balancing and benchmark the method with monolithic and semi-explicit schemes.
