Gauss-Newton Multilevel Methods for Least-Spuares Finite Element Computations of Variably Saturated Subsurface Flow

摘要

We apply the least-squares mixed finite element framework tothe nonlinear elliqtic problems arising in each time-step of an implicit Euler discretization for variably saturated flow. This approach allows the combination of standard piecewise linear H -conforming finite elements for the hydraulic potential with the H(div)-conforming Raviart-Thomas spaces for the flux. It also provides an a posteriori error estimator which may by used in an adaptive mesh refinement strategy. The resulting nonlinear alge-braic least-squares problems are solved by an inexact Gauss-Newton method using a stopping crite-rion for the inner iteration which is bassed on the change of the linearized lease-squares functional relative to the nonlinear least-squares functional. The inner iteration is carried out using an adaptive multilevel method with a block Gauss-seidel smoothing iteration. For a realistic water table recharge problem, the resuits of computational experiments are presented.