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Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations

Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations
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Year:    2009

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 657–676

Abstract

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.27.5.016

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 657–676

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:    Adaptive edge elements 3D eddy currents equations Convergence analysis Error and oscillation reduction Residual type a posteriori error estimates.

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