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Residual based a posteriori error estimators for eddy current computation

Published online by Cambridge University Press:  15 April 2002

Rudi Beck ,
Ralf Hiptmair ,
Ronald H.W. Hoppe  and
Barbara Wohlmuth
Rudi Beck
Affiliation:
ZIB-Berlin, Takustr. 7, 14195 Berlin, Germany. (beck@sc.zib-berlin.de)
Ralf Hiptmair
Affiliation:
SFB 382, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany. (hiptmair@na.uni-tuebingen.de)
Ronald H.W. Hoppe
Affiliation:
Mathematisches Institut, Universität Augsburg, Universitätsstr. 14, 86159 Augsburg, Germany. (hoppe@math.uni-augsburg.de);
Barbara Wohlmuth
Affiliation:
Mathematisches Institut, Universität Augsburg, Universitätsstr. 14, 86159 Augsburg, Germany. (hoppe@math.uni-augsburg.de);
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Abstract

We consider H(curl;Ω)-elliptic problems that have been discretized bymeans of Nédélec's edge elements on tetrahedral meshes. Suchproblems occur in the numerical computation of eddy currents. From the defectequation we derive localized expressions that can be used as a posteriori error estimators to control adaptiverefinement. Under certain assumptions on material parameters and computational domains, we derive local lower bounds and a global upper bound for the total error measured in the energy norm. The fundamental tool in the numerical analysis is a Helmholtz-type decomposition of the error into an irrotational part and a weakly solenoidal part.

Keywords

Residual based a posteriori error estimationNédélec's edge elementsHelmholtz decompositioneddy currents.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 159 - 182
Copyright
© EDP Sciences, SMAI, 2000

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