Mixed Finite Elements and Newton-type Linearizations for the Solution of Richards' Equation

We present the development of a two-dimensional Mixed-Hybrid Finite Element (MHFE) model for the solution of the nonlinear equation of variably saturated ow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest order Raviart-Thomas (RT 0) elements and is \exactly" mass-conserving. Hybridization is used to overcome the ill-conditioning of the mixed system. The scheme is globally rst order in space. Nevertheless, numerical results employing nonuniform meshes show second order accuracy of the pressure head and normal uxes on speciic grid points. The nonlinear systems of algebraic equations resulting from the MHFE discretization are solved using Picard or Newton iterations. Realistic sample tests show that the MHFE-Newton approach achieves fast convergence in many situations, in particular when a good initial guess is provided by either the Picard scheme or relaxation techniques.