The nonlinear systems obtained by discretizing degenerate parabolic equations
may be hard to solve, especially with Newton's method. In this paper, we apply
to Richards equation a strategy that consists in defining a new primary unknown
for the continuous equation in order to stabilize Newton's method by
parametrizing the graph linking the pressure and the saturation. The resulting
form of Richards equation is then discretized thanks to a monotone Finite
Volume scheme. We prove the well-posedness of the numerical scheme. Then we
show under appropriate non-degeneracy conditions on the parametrization that
Newton\^as method converges locally and quadratically. Finally, we provide
numerical evidences of the efficiency of our approach
