Error analysis for the finite element approximation of the Darcy–Brinkman–Forchheimer model for porous media with mixed boundary conditions

This paper deals with the finite element approximation of Darcy–Brinkman- Forchheimer equation, involving a porous media spatially-varying porosity, mixed boundary condition such as inhomogeneous Dirichlet and traction conditions. We first prove that considered problem has unique solution if source terms are small enough. The convergence Taylor–Hood using interpolation porosity is then proved under similar smallness assumptions. Some optimal error estimates obtained to Darcy–Brinkman–Forchheimer model smooth end this by providing fixed-point method solve discrete non-linear problems some numerical experiments make more precise assumptions on illustrate theoretical results.