A finite element method for a unidimensional single-phase nonlinear free boundary problem in groundwater flow

Consider a unidimensional, single-phase nonlinear Stefan problem with nonli near source and permeance terms, and a Dirichlet boundary condition dependi ng on the free boundary function. This problem is important in groundwater flow. By immobilizing the free boundary with the help of a Landau-type tran sformation, together with a homogeneous transformation dealing with the non homogeneous Dirichlet boundary condition, an H-1-finite element method for the problem is proposed and analyzed. Global existence of the approximate s olution is established, and optimal error estimates in L-2, L infinity, H-1 , and H-2 norms are derived for both semi-discrete and fully discrete schem es.