Analysis of a finite volume-finite element method for Darcy-Brinkman two-phase flows in porous media

In this paper, we are interested in the displacement of two incompressible phases in a Darcy-Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a combined finite volume-nonconforming finite element scheme together with a phase-by-phase upstream according to the total velocity.