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

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Knabner P, Rannacher R
Zeitschrift: Vietnam Journal of Mathematics
Jahr der Veröffentlichung: 2017
Heftnummer: 45
Seitenbereich: 179-198
ISSN: 0866-7179
eISSN: 2305-221X
Sprache: Englisch


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Knabner, Peter Prof. Dr.
Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)


Einrichtungen weiterer Autorinnen und Autoren

Ruprecht-Karls-Universität Heidelberg


Zitierweisen

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://dx.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.

BibTeX: 

Zuletzt aktualisiert 2019-19-08 um 13:10