We present an iterative coupling scheme for the numerical approximation of the mixed hyperbolic-parabolic system of fully dynamic poroelasticity. We prove its convergence in the Banach space setting for an abstract semi-discretization in time that allows the application of the family of diagonally implicit Runge-Kutta methods. Recasting the semi-discrete solution as the minimizer of a properly defined energy functional, the proof of convergence uses its alternating minimization. The scheme is closely related to the undrained split for the quasi-static Biot system.
@article{arxiv.1912.05174,
title = {Iterative Coupling for Fully Dynamic Poroelasticity},
author = {Markus Bause and Jakub W. Both and Florin A. Radu},
journal= {arXiv preprint arXiv:1912.05174},
year = {2021}
}