Modified edge finite elements for photonic crystals

Boffi, Daniele; Conforti, Matteo; Gastaldi, Lucia

doi:10.1007/s00211-006-0037-y

Cited by 31 publications

(20 citation statements)

References 18 publications

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“…There are already a number of papers about low order finite element methods for PCs [5,9,11,12] and most recently there has been considerable interest in h, p and hp methods [19,14,25,35,34]. Accurate computations based on a priori hp refinement strategies are shown in [35,34].…”

Section: Introductionmentioning

confidence: 99%

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

Giani

2012

Computing

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Further information on publisher's website:http://dx.doi.org/10.1007/s00607-012-0244-6Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00607-012-0244-6Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications Stefano GianiAbstract 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.

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Section: Introductionmentioning

confidence: 99%

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

Giani

2012

Computing

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“…Our main result in this section is to derive a sharper L 2 -estimate which requires less regularity on curl v (in particular, no additional requirements when v ∈ H s with s > 1) (see also [6]). …”

Section: Interpolation Estimates For Edge Elementsmentioning

confidence: 99%

Interpolation estimates for edge finite elements and application to band gap computation

Boffi¹,

Gastaldi

2006

Applied Numerical Mathematics

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“…There are already a number of papers about low order finite element methods for PCs [4,10,14,15,24,28] and most recently there has been considerable interest in p and hp methods, with the latter having the potential to obtain exponential accuracy [16,32,39,40] . Accurate computations based on a priori hp refinement strategies are shown in [39,40].…”

Section: Introductionmentioning

confidence: 99%