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Flow in variably saturated porous media is typically modeled 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 [1] , 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. [ABSTRACT FROM AUTHOR]

Abstract We analyze a fully discrete numerical scheme for the model describing two-phase immiscible flow in porous media with dynamic effects in the capillary pressure. We employ the Euler implicit method for the time discretization. The spatial discretization is based on the mixed finite element method (MFEM). Specifically, the lowest order Raviart–Thomas elements are applied. In this paper, the error estimates for the saturation, fluxes and phase pressures in L ∞ (0 , T ; L 2 (Ω)) are derived for the temporal and spatial discretization to show the convergence of the scheme. Finally, we present some numerical results to support the theoretical findings. [ABSTRACT FROM AUTHOR]