A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity

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• 作者：Peter Knabner ; Rolf Rannacher
• 关键词：Degenerate parabolic problem ; Non ; Lipschitzian nonlinearity ; Finite element method ; Pointwise error ; Porous media flow
• 刊名：Vietnam Journal of Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：45
• 期：1-2
• 页码：179-198
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2305-2228
• 卷排序：45

文摘

This paper deals with the numerical approximation of certain degenerate parabolic systems arising from flow problems in porous media with slow adsorption. The characteristic difficulty of these problems comes from their monotone but non-Lipschitzian nonlinearity. For a model problem of this type, optimal-order pointwise error estimates are derived for the spatial semi-discretization by the finite element Galerkin method. The proof is based on linearization through a parabolic duality argument in L_∞(L_∞) spaces and corresponding sharp L₁ estimates for regularized parabolic Green functions.