A Nite Element Method for a Unidimensional Single-phase Nonlinear Free Boundary Problem in Groundwater Ow
نویسندگان
چکیده
Consider a unidimensional, single-phase nonlinear Stefan problem with nonlinear source and permeance terms, and a Dirichlet boundary condition depending on the free-boundary function. This problem is important in groundwater ow. By immobilizing the free-boundary with the help of a Landau type transformation, together with a homogeneous transformation dealing with the nonhomogeneous Dirichlet boundary condition , an H 1-nite element method for the problem is proposed and analysed. Global existence of the approximate solution is established, and optimal error estimates in L 2 , L 1 ; H 1 and H 2 norms are derived for both semi-discrete and fully discrete schemes.
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