A Review of Unified A Posteriori Finite Element Error Control

  • This paper aims at a general guideline to obtain a posteriori error estimates for the finite element error control in computational partial differential equations. In the abstract setting of mixed formulations, a generalised formulation of the corresponding residuals is proposed which then allows for the unified estimation of the respective dual norms. Notably, this can be done with an approach which is applicable in the same way to conforming, nonconforming and mixed discretisations. Subsequently, the unified approach is applied to various model problems. In particular, we consider the Laplace, Stokes, Navier-Lame, and the semi-discrete eddy current equations.

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Author:Carsten CarstensenGND, Martin Eigel, Caroline Löbhard, Ronald H. W. HoppeGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1450
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-13)
Publishing Institution:Universität Augsburg
Contributing Corporation:Humboldt Universität zu Berlin, Yonsei University Seoul, University of Houston
Release Date:2010/10/12
Tag:unified a posteriori error analysis; finite element method; adaptive algorithms; residual estimators
GND-Keyword:Partielle Differentialgleichung; Finite-Elemente-Methode; A-posteriori-Abschätzung; Fehleranalyse
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand