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The nonlinear systems obtained by discretizing degenerate parabolic equationsmay be hard to solve, especially with Newton's method. In this paper, we applyto Richards equation a strategy that consists in defining a new primary unknownfor the continuous equation in order to stabilize Newton's method byparametrizing the graph linking the pressure and the saturation. The resultingform of Richards equation is then discretized thanks to a monotone FiniteVolume scheme. We prove the well-posedness of the numerical scheme. Then weshow under appropriate non-degeneracy conditions on the parametrization thatNewton\^as method converges locally and quadratically. Finally, we providenumerical evidences of the efficiency of our approach.

Improving Newton's method performance by parametrization: the case of Richards equation