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 non-linear equation of variably satur ated flow in groundwater on unstructured triangular meshes. By this approac h the Darcy velocity is approximated using lowest-order Raviart-Thomas (RT0 ) elements and is 'exactly' mass conserving. Hybridization is used to overc ome the ill-conditioning of the mixed system. The scheme is globally first- order in space. Nevertheless, numerical results employing non-uniform meshe s show second-order accuracy of the pressure head and normal fluxes on spec ific grid points. The non-linear systems of algebraic equations resulting f rom the MHFE discretization are solved using Picard or Newton iterations. R ealistic sample tests show that the MHFE-Newton approach achieves fast conv ergence in many situations, in particular, when a good initial guess is pro vided by either the Picard scheme or relaxation techniques. Copyright (C) 1 999 John Wiley & Sons, Ltd.