A Least Squares Mixed Finite Element Method For

For the coupling of ow and deformation in variably saturated porous media we propose a mixed nite element method based on a least-squares principle. This approach is motivated by the fact that all process variables, i.e., hydraulic potential and uid ux as well as displacement eld and stress tensor, are approximated directly by suitable nite element spaces. For the ow model we consider both fully saturated and variably saturated porous media. The deformation is assumed to be linearly elastic. Our approach combines a least-squares approach for variably saturated subsurface ow with a recently developed least-squares formulation for linear elasticity. Standard -conforming piecewise linear and quadratic nite elements are used for the hydraulic potential and for (each component of) the displacement, respectively. For the ux and stress components, the H(div)-conforming Raviart-Thomas spaces (of lowest order) are used. Computational results are presented for some test problems including two-dimensional fully saturated and one-dimensional variably saturated problems