Mathematical model
==================

The computational algorithm is based upon a consistent incremental formulation
in the Eulerian framework, such that the incremental formulation uses the
updated Lagrangian approach. The formulation is based on a quasi­static
perturbation of the medium described by the Biot model which is constituted by
poroelastic coefficients and the permeability governing the Darcy flow. The
equilibrium equation and the mass conservation are expressed in the spatial,
deformed configuration. Using the material derivative with respect to a
convection velocity field, a rate formulation is derived which allows to
approximate the residuum function associated with the unknown configuration
using the last known configuration. The time­space discretization is based on an
implicit time­integration scheme and conforming finite element approximation. A
multistep approach uses a combination of the forward and backward finite
differences. As an option, the Newmark integration scheme can be selected. The
theoretical background and numerical tests have been published in:

*Eduard Rohan, Vladimír Lukeš*, Modeling large­deforming fluid­saturated porous
media using an Eulerian incremental formulation, In *Advances in Engineering
Software*, 2016, `DOI:10.1016/j.advengsoft.2016.11.003 <https://doi.org/10.1016/j.advengsoft.2016.11.003>`_,
`arXiv:1610.05103 <https://arxiv.org/abs/1610.05103v1>`_.