Robust a posteriori error estimation for finite element approximation to H(curl) problem
Abstract
In this work, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H (curl) problem with inhomogeneous media and with the righthand side only in L^{2}. The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H (curl) problem. An alternate way of recovery is presented as well by localizing of the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasimonotonicity assumption. Lastly, we present numerical results for several H (curl) interface problems.
 Authors:

 Purdue Univ., West Lafayette, IN (United States). Department of Mathematics
 Pennsylvania State Univ., University Park, PA (United States). Department of Mathematics
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1466146
 Alternate Identifier(s):
 OSTI ID: 1326255
 Report Number(s):
 LLNLJRNL733144
Journal ID: ISSN 00457825; 884835
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Volume: 309; Journal Issue: C; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Maxwell’s equations; Nédélec finite elements; A posteriori error estimation; Interface problem; Flux recovery; Duality error estimation
Citation Formats
Cai, Zhiqiang, Cao, Shuhao, and Falgout, Rob. Robust a posteriori error estimation for finite element approximation to H(curl) problem. United States: N. p., 2016.
Web. https://doi.org/10.1016/j.cma.2016.06.007.
Cai, Zhiqiang, Cao, Shuhao, & Falgout, Rob. Robust a posteriori error estimation for finite element approximation to H(curl) problem. United States. https://doi.org/10.1016/j.cma.2016.06.007
Cai, Zhiqiang, Cao, Shuhao, and Falgout, Rob. Thu .
"Robust a posteriori error estimation for finite element approximation to H(curl) problem". United States. https://doi.org/10.1016/j.cma.2016.06.007. https://www.osti.gov/servlets/purl/1466146.
@article{osti_1466146,
title = {Robust a posteriori error estimation for finite element approximation to H(curl) problem},
author = {Cai, Zhiqiang and Cao, Shuhao and Falgout, Rob},
abstractNote = {In this work, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H (curl) problem with inhomogeneous media and with the righthand side only in L2. The estimator is of the recovery type. Independent with the current approximation to the primary variable (the electric field), an auxiliary variable (the magnetizing field) is recovered in parallel by solving a similar H (curl) problem. An alternate way of recovery is presented as well by localizing of the error flux. The estimator is then defined as the sum of the modified element residual and the residual of the constitutive equation defining the auxiliary variable. It is proved that the estimator is approximately equal to the true error in the energy norm without the quasimonotonicity assumption. Lastly, we present numerical results for several H (curl) interface problems.},
doi = {10.1016/j.cma.2016.06.007},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 309,
place = {United States},
year = {2016},
month = {6}
}