Adaptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems

  • We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin (IPDG-H) method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents equations. The method can be derived from a mixed formulation of the given boundary value problem and involves a Lagrange multiplier that is an approximation of the tangential traces of the primal variable on the interfaces of the underlying triangulation of the computational domain. It is shown that the IPDG-H technique can be equivalently formulated and thus implemented as a mortar method. The mesh adaptation is based on a residual-type a posteriori error estimator consisting of element and face residuals. Within a unified framework for adaptive finite element methods, we prove the reliability of the estimator up to a consistency error. The performance of the adaptive symmetric IPDG-H method is documented by numerical results for representative test examples in 2D.

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Author:Carsten CarstensenGND, Ronald H. W. HoppeORCiDGND, Natasha S. Sharma, Tim Warburton
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-06)
Publishing Institution:Universität Augsburg
Contributing Corporation:Humboldt Universität zu Berlin, Yonsei University, University of Houston, Rice University
Release Date:2010/04/27
Tag:adaptive hybridized Interior Penalty Discontinuous Galerkin method; a posteriori error analysis; H(curl)-elliptic boundary value problems
GND-Keyword:Elliptisches Randwertproblem; Finite-Elemente-Methode; Diskontinuierliche Galerkin-Methode; Fehleranalyse; A-posteriori-Abschätzung
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