Mixed finite elements for the solution of Richard's equation

We present a two-dimensional mixed finite element model of variably saturated flow on unsaturated triangular meshes. Velocities are approximated using the lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard iterations in combination with ad hoc preconditioning techniques to improve the convergence of the conjugate gradient method in the solution of the linearized mixed system. The MFE scheme with Picard linearizations is tested on a sample test and compared with the Galerkin Finite Element formulation. The comparison is carried out in terms of convergence of the nonlinear and linear solvers, and computational efficiency.