Residual based a posteriori error estimators for Eddy current computation

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

doi:10.1051/m2an:2000136

Residual based a posteriori error estimators for Eddy current computation

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

Research output: Contribution to journal › Article › peer-review

174 Scopus citations

Abstract

We consider H (curl; Ω)-elliptic problems that have been discrelized 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 uppex 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.

Original language	English
Pages (from-to)	159-182
Number of pages	24
Journal	Mathematical Modelling and Numerical Analysis
Volume	34
Issue number	1
DOIs	https://doi.org/10.1051/m2an:2000136
State	Published - 2000
Externally published	Yes

Keywords

Eddy currents
Helmholtz decomposition
Nédélec's edge elements
Residual based a posteriori error estimation

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10.1051/m2an:2000136

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abstract = "We consider H (curl; Ω)-elliptic problems that have been discrelized by means of N{\'e}d{\'e}lec'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 uppex 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 = "Eddy currents, Helmholtz decomposition, N{\'e}d{\'e}lec's edge elements, Residual based a posteriori error estimation",

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T1 - Residual based a posteriori error estimators for Eddy current computation

AU - Beck, Rudi

AU - Hiptmair, Ralf

AU - Hoppe, Ronald H.W.

AU - Wohlmuth, Barbara

PY - 2000

Y1 - 2000

N2 - We consider H (curl; Ω)-elliptic problems that have been discrelized 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 uppex 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.

AB - We consider H (curl; Ω)-elliptic problems that have been discrelized 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 uppex 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.

KW - Eddy currents

KW - Helmholtz decomposition

KW - Nédélec's edge elements

KW - Residual based a posteriori error estimation

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DO - 10.1051/m2an:2000136

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SN - 0764-583X

VL - 34

SP - 159

EP - 182

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 1

ER -

Residual based a posteriori error estimators for Eddy current computation

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Keywords

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