  Flow in variably saturated porous media is typically modelled by the Richards
equation, a nonlinear elliptic-parabolic equation which is notoriously
challenging to solve numerically. In this paper, we propose a robust and fast
iterative solver for Richards' equation. The solver relies on an adaptive
switching algorithm, based on rigorously derived a posteriori indicators,
between two linearization methods: L-scheme and Newton. Although a combined
L-scheme/Newton strategy was introduced previously in [List & Radu (2016)],
here, for the first time we propose a reliable and robust criteria for
switching between these schemes. The performance of the solver, which can be in
principle applied to any spatial discretization and linearization methods, is
illustrated through several numerical examples.
