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

Giani, S.

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


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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.

Citation

Giani, S. (2013). An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications. Computing, 95(5), 395-414. https://doi.org/10.1007/s00607-012-0244-6

Journal Article Type Article
Acceptance Date Nov 16, 2012
Publication Date May 1, 2013
Deposit Date Feb 12, 2013
Publicly Available Date Mar 28, 2024
Journal Computing
Print ISSN 0010-485X
Electronic ISSN 1436-5057
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 95
Issue 5
Pages 395-414
DOI https://doi.org/10.1007/s00607-012-0244-6
Keywords Eigenvalue problem, Finite element method, hp-adaptivity, A posteriori error estimator, Photonic crystals.

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