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An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications.

Giani, S. (2013) 'An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications.', Computing., 95 (5). pp. 395-414.

Abstract

In this paper we propose and analyse an error estimator suitable for \(hp\)-adaptive continuous finite element methods for computing the band structure and the isolated modes of 2D photonic crystal (PC) applications. The error estimator that we propose is based on the residual of the discrete problem and we show that it leads to very fast convergence in all considered examples when used with \(hp\)-adaptive refinement techniques. In order to show the flexibility and robustness of the error estimator we present an extensive collection of numerical experiments inspired by real applications. In particular we are going to consider PCs with point defects, PCs with line defects, bended waveguides and semi-infinite PCs.

Item Type:Article
Keywords:Eigenvalue problem, Finite element method, hp-adaptivity, A posteriori error estimator, Photonic crystals.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/s00607-012-0244-6
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0244-6
Date accepted:16 November 2012
Date deposited:13 October 2015
Date of first online publication:May 2013
Date first made open access:No date available

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