A Posteriori Error Analysis of Hybridized Mixed Finite Element Methods for Second Order Elliptic Boundary Value Problems

  • The mixed hybrid finite element approximation of second order elliptic boundary value problems by hybridized Raviart-Thomas elements of any order can be seen as a nonconforming approximation of the primal mixed formulation of the problem. In this paper, we provide a unified framework for the a posteriori error analysis in terms of residual-type a posteriori error estimators consisting of element and face (edge) residuals. This unified framework allows to establish the reliability of the error estimators on the basis of appropriate interpolation operators as well as suitable reconstruction operators.

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Author:Ronald H. W. HoppeORCiDGND, Johannes Neher, Natasha S. Sharma
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1220
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-01)
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston
Release Date:2009/01/22
Tag:adaptive hybridized mixed finite element methods; a posteriori error analysis; elliptic boundary value problems
GND-Keyword:Finite-Elemente-Methode; A-posteriori-Abschätzung; Fehleranalyse; Elliptisches Randwertproblem
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