Mixed Element Method for Two-Dimensional Darcy-Forchheimer Model

Abstract

A mixed element method is introduced to solve Darcy-Forchheimer equation, in which the velocity and pressure are approximated by mixed element such as Raviart-Thomas, Brezzi-Douglas-Marini element. We establish the existence and uniqueness of the problem. Error estimates are presented based on the monotonicity owned by the Forchheimer term. An iterative scheme is given for practical computation. The numerical experiments using the lowest order Raviart-Thomas (RT0) mixed element show that the convergence rates of our method are in agree with the theoretical analysis.