A mixed element analysis of the Biot's model with <scp>Darcy–Forchheimer</scp> flow

In this article, we consider the three-field Biot's consolidation model, in which the flow's velocity is described by Darcy–Forchheimer law. The model is nonlinear and the unknown variables are the displacement of the solid phase, fluid flux, and pore pressure. The linear finite element is proposed to approximate the solid displacement and the RT mixed finite element is proposed to approximate the fluid flux and pore pressure. The error estimates is given for semidiscrete scheme and fully discrete scheme. When analyzing the fully discrete scheme, no time step restriction is needed. Numerical tests for this method confirm the accuracy of the P1-RT0-P0 method when the constraint storage coefficient c 0 $$ {c}_0 $$ is positive and c 0 $$ {c}_0 $$ is null.