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Title: 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 right-hand 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 quasi-monotonicity assumption. Lastly, we present numerical results for several H (curl) interface problems.

Authors:
 [1];  [2];  [3]
  1. Purdue Univ., West Lafayette, IN (United States). Department of Mathematics
  2. Pennsylvania State Univ., University Park, PA (United States). Department of Mathematics
  3. 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):
LLNL-JRNL-733144
Journal ID: ISSN 0045-7825; 884835
Grant/Contract Number:  
AC52-07NA27344
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 0045-7825
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. doi: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. doi: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. doi: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 right-hand 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 quasi-monotonicity 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}
}

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