Mixed finite elements for the solution of the variably saturated flow equation

In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations. Theroretical superconvergence properties of the RT0 approach are experimented on analytical sample problems. It is shown that second order convergence on the pressure head and velocity fields can be obtained at particular points of the triangulation also on nonuniform meshes. Simulations on a realistic sample test show that the Newton approach achieves fast convergence if a good initial guess is provided by either the Picard scheme or relaxation techniques.