Least-squares mixed finite element solution of variably saturated subsurface flow problems

A least-squares mixed finite element formulation is applied to the nonlinea r elliptic problems arising in each time-step of an implicit Euler discreti zation for variably saturated ow problems. This approach simultaneously con structs approximations to the flux in Raviart-Thomas spaces and to the hydr aulic potential by standard H-1-conforming linear finite elements. Two impo rtant properties of the least-squares approach are investigated in detail: the local least-squares functional provides an a posteriori error estimator and Gauss Newton methods are robust iterative solvers for the resulting no nlinear least-squares problems. Computational experiments conducted for a r ealistic water table recharge problem illustrate the effectiveness of this approach.