Least-Squares Mixed Finite Element Solution of Variably Saturated Subsurface Flow Problems

A least-squares mixed nite element formulation is applied to the nonlinear elliptic problems arising in each time-step of an implicit Euler discretization for variably saturated ow problems. This approach simultaneously constructs approximations to the ux in Raviart-Thomas spaces and to the hydraulic potential by standard H 1-conforming linear nite elements. Two important 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 nonlinear least-squares problems. Computational experiments conducted for a realistic water table recharge problem illustrate the eeectiveness of this approach.