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Volume 27, Issue 5
Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations

R.H.W. Hoppe & J. Schöberl

DOI: 10.4208/jcm.2009.27.5.016

J. Comp. Math., 27 (2009), pp. 657-676.

Published online: 2009-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65F10, 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-27-657, author = {R.H.W. Hoppe and J. Schöberl}, title = {Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.5.016}, url = {http://global-sci.org/intro/article_detail/jcm/8595.html} }
TY - JOUR T1 - Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations AU - R.H.W. Hoppe & J. Schöberl JO - Journal of Computational Mathematics VL - 5 SP - 657 EP - 676 PY - 2009 DA - 2009/10 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.5.016 UR - https://global-sci.org/intro/article_detail/jcm/8595.html KW - Adaptive edge elements, 3D eddy currents equations, Convergence analysis, Error and oscillation reduction, Residual type a posteriori error estimates. AB -

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.

R.H.W. Hoppe and J. Schöberl. (2009). Convergence of Adaptive Edge Element Methods for the 3D Eddy Currents Equations. Journal of Computational Mathematics. 27 (5). 657-676. doi:10.4208/jcm.2009.27.5.016
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