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

摘要

A least-squares mixed finite 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 flux in Raviart-Thomas spaces and to the hydraulic potential by standard H-1-conforming linear finite 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 effectiveness of this approach. [References: 31]