Robust A Posteriori Error Estimation for Finite Element Approximation to H(curl) Problem

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 L^2. The estimator is of the recovery type. Independent with the current approximation to the primary...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Cai, Zhiqiang, Cao, Shuhao, Falgout, Rob
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.06.2016
Subjects
Approximation
Constitutive equations
Constitutive relationships
Electric fields
Errors
Finite element method
Inhomogeneous media
Mathematical analysis
Mathematics - Numerical Analysis
Recovery
Robustness (mathematics)
Online AccessGet full text

Cover

More Information
Summary: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 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 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 two H(curl) interface problems.
ISSN:2331-8422
DOI:10.48550/arxiv.1510.00027