Iterative solvers for Biot model under small and large deformations

@article{Revern2020IterativeSF,
  title={Iterative solvers for Biot model under small and large deformations},
  author={Manuel Antonio Borregales Rever{\'o}n and Kundan Kumar and J. Nordbotten and F. Radu},
  journal={Computational Geosciences},
  year={2020},
  volume={25},
  pages={687 - 699}
}
We consider L-scheme and Newton-based solvers for Biot model under large deformation. The mechanical deformation follows the Saint Venant-Kirchoff constitutive law. Furthermore, the fluid compressibility is assumed to be non-linear. A Lagrangian frame of reference is used to keep track of the deformation. We perform an implicit discretization in time (backward Euler) and propose two linearization schemes for solving the non-linear problems appearing within each time step: Newton’s method and L… Expand
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