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

Zhiqiang Cai, Shuhao Cao, Rob Falgout

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)182-201
Number of pages20
JournalComputer Methods in Applied Mechanics and Engineering
Volume309
DOIs
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

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