A finite element method for a unidimensional single-phase nonlinear free boundary problem in groundwater flow |
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Authors: | Liang D; Zhang B |
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Institution: |
A1 School of Mathematics and System Sciences, Shandong University, Jinan? 250100, PRC A2 School of Mathematical and Information Sciences, Coventry University, Coventry CV1 5FB, UK
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Abstract: | Consider a unidimensional, single-phase nonlinear Stefan problemwith nonlinear source and permeance terms, and a Dirichlet boundarycondition depending on the free boundary function. This problemis important in groundwater flow. By immobilizing the free boundarywith the help of a Landau-type transformation, together witha homogeneous transformation dealing with the nonhomogeneousDirichlet boundary condition, an H1-finite element method forthe problem is proposed and analyzed. Global existence of theapproximate solution is established, and optimal error estimatesin L2, L, H1 and H2 norms are derived for both semi-discreteand fully discrete schemes. |
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