A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity
Knabner P, Rannacher R (2017)
Publication Language: English
Publication Type: Journal article
Publication year: 2017
Journal
Pages Range: 179-198
Journal Issue: 45
URI: https://link.springer.com/content/pdf/10.1007/s10013-016-0214-y.pdf
DOI: 10.1007/s10013-016-0214-y
Open Access Link: https://link.springer.com/content/pdf/10.1007/s10013-016-0214-y.pdf
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 L1 estimates for regularized parabolic Green functions.
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Germany (DE)How to cite
APA:
Knabner, P., & Rannacher, R. (2017). A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity. Vietnam Journal of Mathematics, 45, 179-198. https://doi.org/10.1007/s10013-016-0214-y
MLA:
Knabner, Peter, and Rolf Rannacher. "A Priori Error Analysis for the Galerkin Finite Element Semi-discretization of a Parabolic System with Non-Lipschitzian Nonlinearity." Vietnam Journal of Mathematics 45 (2017): 179-198.
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