A multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models

We develop a multipoint flux mixed finite element method for the compressible Darcy-Forchheimer models. This method is motivated by the multipoint flux approximation method. Based on the lowest order Brezzi-Douglas-Marini mixed finite element method and combined with a special quadrature rule that allows for local velocity elimination and leads to a cell-centered system for the pressures. We develop two approximation methods for the problems, the semi-discrete method and fully discrete method, where the fully discrete method includes the backward Euler scheme and the Crank-Nicolson scheme. Theoretical results show the convergences for both pressure and velocity. The numerical experiments show that the convergence rates of the method are in agreement with the theoretical analysis.