Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem
Numerical Analysis
2016-02-02 v1
Abstract
We present an a posteriori estimator of the error in the L^2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of N\'ed\'elec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L^2-orthogonal projection of the exact eigenfunction onto the curl of the N\'ed\'elec finite element space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms and local efficiency of the error indicators is shown by using a standard bubble functions technique. The behavior of the a posteriori error estimator is illustrated on a numerical test.
Cite
@article{arxiv.1602.00675,
title = {Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem},
author = {Daniele Boffi and Lucia Gastaldi and Rodolfo Rodríguez and Ivana Šebestová},
journal= {arXiv preprint arXiv:1602.00675},
year = {2016}
}