Residual based a posteriori error estimators for eddy current computation

Rudi Beck; Ralf Hiptmair; Ronald H.W. Hoppe; Barbara Wohlmuth

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 1, page 159-182
  • ISSN: 0764-583X

Abstract

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We consider H(curl;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. 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.

How to cite

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Beck, Rudi, et al. "Residual based a posteriori error estimators for eddy current computation." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 159-182. <http://eudml.org/doc/197591>.

@article{Beck2010,
abstract = { We consider H(curl;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. 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. },
author = {Beck, Rudi, Hiptmair, Ralf, Hoppe, Ronald H.W., Wohlmuth, Barbara},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Residual based a posteriori error estimation; Nédélec's edge elements; Helmholtz decomposition; eddy currents.; finite element method; error bounds; eddy currents; mesh refinement},
language = {eng},
month = {3},
number = {1},
pages = {159-182},
publisher = {EDP Sciences},
title = {Residual based a posteriori error estimators for eddy current computation},
url = {http://eudml.org/doc/197591},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Beck, Rudi
AU - Hiptmair, Ralf
AU - Hoppe, Ronald H.W.
AU - Wohlmuth, Barbara
TI - Residual based a posteriori error estimators for eddy current computation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 159
EP - 182
AB - We consider H(curl;Ω)-elliptic problems that have been discretized by means of Nédélec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From the defect equation we derive localized expressions that can be used as a posteriori error estimators to control adaptive refinement. 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.
LA - eng
KW - Residual based a posteriori error estimation; Nédélec's edge elements; Helmholtz decomposition; eddy currents.; finite element method; error bounds; eddy currents; mesh refinement
UR - http://eudml.org/doc/197591
ER -

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