TY - JOUR

T1 - Robust a posteriori error estimation for finite element approximation to H(curl) problem

AU - Cai, Zhiqiang

AU - Cao, Shuhao

AU - Falgout, Rob

N1 - Funding Information:
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 ( LLNL-JRNL-645325 ). This work was supported in part by the National Science Foundation under grants DMS-1217081 , DMS-1320608 , DMS-1418934 , and DMS-1522707 .
Publisher Copyright:
© 2016 Elsevier B.V.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - In this paper, 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. Finally, we present numerical results for several H(curl) interface problems.

AB - In this paper, 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. Finally, we present numerical results for several H(curl) interface problems.

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U2 - 10.1016/j.cma.2016.06.007

DO - 10.1016/j.cma.2016.06.007

M3 - Article

AN - SCOPUS:84976877773

VL - 309

SP - 182

EP - 201

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -