Vietnam Journal of Mathematics

, Volume 45, Issue 1–2, pp 179–198 | Cite as

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

  • Peter Knabner
  • Rolf RannacherEmail author


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 L 1 estimates for regularized parabolic Green functions.


Degenerate parabolic problem Non-Lipschitzian nonlinearity Finite element method Pointwise error Porous media flow 

Mathematics Subject Classification (2010)

65M15 35K65 35R35 76S05 


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Lehrstuhl für Angewandte Mathematik IUniversität Erlangen-Nürnberg, Department MathematikErlangenGermany
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany

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