We consider a non-linear extension of Biot's model for poromechanics, wherein both the fluid flow and mechanical deformation are allowed to be non-linear. We perform an implicit discretization in time (backward Euler) and propose two iterative schemes for solving the non-linear problems appearing within each time step: a splitting algorithm extending the undrained split and fixed stress methods to non-linear problems, and a monolithic L-scheme. The convergence of both schemes is shown rigorously. Illustrative numerical examples are presented to confirm the applicability of the schemes and validate the theoretical results.
@article{arxiv.1702.00328,
title = {Robust iterative schemes for non-linear poromechanics},
author = {Manuel Borregales and Florin A. Radu and Kundan Kumar and Jan M. Nordbotten},
journal= {arXiv preprint arXiv:1702.00328},
year = {2017}
}