Parameter-robust mixed element method for poroelasticity with Darcy-Forchheimer flow

In this paper, the Biot's consolidation model is considered, and Darcy-Forchheimer equation is used to describe the relationship between the fluid velocity and pressure. The model is nonlinear and the unknown variables are the solid displacement, the fluid velocity and pressure. The Bernardi-Raugel element is used for displacement and the RT mixed element is used for the fluid velocity and pressure. The parameter-robust BR-RT0-P0 method presented here is uniformly stable not only with respect to the Lame constant lambda$$ \lambda $$, but also with respect to the constrained specific storage coefficient c0$$ {c}_0 $$. We demonstrate the well-posedness of the BR-RT0-P0 finite element solutions, and give the error estimates of the finite element approximations using the monotonicity of the nonlinear Forchheimer term. The error estimates are divided into two cases, that is, c0$$ {c}_0 $$ is positive and c0$$ {c}_0 $$ is nonnegative. Numerical experiments are presented to verify theoretical analysis. Moreover we focus on the variation of pressure by several poroelasticity problems.