A priori error analysis for the Galerkin finite element semi-discretization of a parabolic system with non-Lipschitzian nonlinearity
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, op...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2017
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| In: |
Vietnam journal of mathematics
Year: 2016, Volume: 45, Issue: 1-2, Pages: 179-198 |
| ISSN: | 2305-2228 |
| DOI: | 10.1007/s10013-016-0214-y |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s10013-016-0214-y Verlag, Volltext: https://link.springer.com/article/10.1007/s10013-016-0214-y 
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| Author Notes: | Peter Knabner, Rolf Rannacher |
| Summary: | 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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| Item Description: | Published online: 16 August 2016 Gesehen am 30.01.2018 |
| Physical Description: | Online Resource |
| ISSN: | 2305-2228 |
| DOI: | 10.1007/s10013-016-0214-y |