Iterative Scheme for the Darcy-Forchheimer Problem with Pressure Boundary Condition

This paper addresses the Darcy-Forchheimer problem with pressure boundary conditions. We employ finite element methods to discretize the system and introduce an iterative scheme to solve the resulting nonlinear discrete problem. The well-posedness and convergence of this iterative approach are then demonstrated. Finally, we present several numerical experiments to validate the proposed numerical schemes.