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

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Abstract

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.

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Authors and Affiliations

  1. Lehrstuhl für Angewandte Mathematik I, Universität Erlangen-Nürnberg, Department Mathematik, Cauerstr. 11, 91058, Erlangen, Germany

    Peter Knabner

  2. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 205 (Mathematikon), 69120, Heidelberg, Germany

    Rolf Rannacher

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  1. Peter Knabner
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  2. Rolf Rannacher
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Correspondence to Rolf Rannacher.

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This article is dedicated to Willi Jäger at the occasion of his 75th birthday.

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Knabner, P., Rannacher, R. A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity. Vietnam J. Math. 45, 179–198 (2017). https://doi.org/10.1007/s10013-016-0214-y

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  • DOI: https://doi.org/10.1007/s10013-016-0214-y

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