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In this work, we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate parabolic equation and an elliptic one. The proposed numerical scheme is based on backward Euler for the temporal discretization and mixed finite element method for the spatial one. A priori stability and error estimates are presented to prove the convergence of the scheme. A monotone increasing, Hölder continuous saturation is considered. The convergence of the scheme is naturally dependant on the Hölder exponent. The nonlinear systems within each time step are solved by a robust linearization method, called the -scheme. This iterative method does not involve any regularization step. The convergence of the -scheme is rigorously proved under the assumption of a Lipschitz continuous saturation. For the Hölder …