Convergence of adaptive edge element methods for the 3D eddy currents equations

  • We consider an Adaptive Edge Finite Element Method (AEFEM) for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.

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Author:Ronald H. W. HoppeORCiDGND, Joachim Schöberl
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Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-38)
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston ; RWTH Aachen
Release Date:2007/10/26
Tag:computational electromagnetics; adaptive edge elements; convergence analysis; eddy currents equations
GND-Keyword:Elektromagnetismus; Finite-Elemente-Methode; Anpassung <Mathematik>; Konvergenz; Wirbelstrom
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