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

Abstract 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.

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